CBSETUTOR.aiCBSETUTOR.ai
India's #1 AI TutorClass 8 · Mathematics · Chapter 5

CBSE Class 8 Mathematics — Squares and Square Roots: complete chapter guide

CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots marks a turning point where arithmetic transitions into algebraic thinking. Every year, approximately 1.8 million Class 8 CBSE students encounter this chapter, which lays the groundwork for quadratic equations, Pythagoras theorem applications, and mensuration in higher classes. The NCERT textbook structures this chapter across four exercises with 34 questions total, progressing from pattern recognition in perfect squares to calculating square roots of five-digit numbers using long division. Students often struggle with the long division method initially because it reverses the familiar division algorithm, but the technique becomes intuitive after solving 15-20 problems systematically.

Your child's private AI tutor — trained on NCERT.
3-day free trial · ₹1 to start · Cancel anytime.
Start 3-day free trial →

Key takeaways

  • ✓CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots covers properties of square numbers, Pythagorean triplets, and two calculation methods for square roots.
  • ✓A square number ending in 2, 3, 7, or 8 can never be a perfect square — this property helps quickly eliminate wrong answers in competitive exams.
  • ✓Pythagorean triplets follow the pattern (2m, m²−1, m²+1) for any natural number m > 1, generating sets like (6, 8, 10) and (8, 15, 17).
  • ✓Prime factorisation method works best for perfect squares, pairing prime factors and taking one from each pair to find the square root.
  • ✓Long division method finds square roots of both perfect and non-perfect squares to any decimal place, essential for Class 10 board problems.
  • ✓Square of a number ending in 5 always ends in 25, and the digits before 25 follow the pattern n(n+1) where n is the tens digit.
  • ✓The chapter carries 8-10 marks in CBSE Class 8 final exams, with 60% weightage on calculation methods and 40% on properties and applications.

What CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots Covers

The NCERT curriculum for CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots divides content into four major topics spread across 12-15 class periods. First, students explore properties of square numbers through pattern observation — discovering why no perfect square ends in 2, 3, 7, or 8, and learning that squares of even numbers are even while squares of odd numbers are odd. Second, the chapter introduces Pythagorean triplets, sets of three natural numbers (a, b, c) where a² + b² = c², teaching the generating formula (2m, m²−1, m²+1). Third, students master finding square roots through prime factorisation, a method that works elegantly for perfect squares by pairing identical prime factors. Fourth, the long division method extends square root calculation to non-perfect squares and large numbers, a technique unique to Indian mathematics curricula and essential for board exam success. Exercise 5.1 contains 9 questions on properties and patterns, Exercise 5.2 has 5 questions on perfect square identification, Exercise 5.3 contains 10 questions on prime factorisation method, and Exercise 5.4 has 10 questions on long division method. The chapter concludes with word problems applying square roots to area calculations and estimation challenges.
  • Exercise 5.1: Properties of square numbers, patterns in units digits, sums of consecutive odd numbers equaling perfect squares
  • Exercise 5.2: Identifying perfect squares, smallest multiplier/divisor to make a number a perfect square
  • Exercise 5.3: Square root by prime factorisation for numbers up to five digits, application to product and quotient of square roots
  • Exercise 5.4: Square root by long division for perfect and non-perfect squares, decimal approximation to required places

Properties of Square Numbers Every Class 8 Student Must Know

CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots begins with seven critical properties that help students identify perfect squares without calculation. Property 1: A number ending in 2, 3, 7, or 8 can never be a perfect square. For example, 123, 457, 1008 are instantly ruled out. Property 2: A perfect square can only end in 0, 1, 4, 5, 6, or 9, but not all numbers ending in these digits are perfect squares (like 20 or 50). Property 3: The number of zeros at the end of a perfect square is always even — 100, 2500, 490000 are perfect squares, but 1000 and 10000 are not (having 3 and 4 zeros respectively). Property 4: For every natural number n, (n+1)² − n² = (n+1) + n, meaning the difference between consecutive squares equals the sum of the two numbers. Property 5: The sum of the first n odd natural numbers equals n². For instance, 1 + 3 + 5 + 7 + 9 = 25 = 5². Property 6: If a number is a perfect square, its prime factorisation contains all exponents as even numbers. Property 7: Between consecutive perfect squares n² and (n+1)², there are exactly 2n non-square natural numbers. These properties appear in 3-4 marks worth of questions in CBSE Class 8 final exams.

Understanding Pythagorean Triplets in Class 8 Mathematics

CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots introduces Pythagorean triplets as sets of three natural numbers (a, b, c) satisfying a² + b² = c². The NCERT textbook provides the generating formula: for any natural number m > 1, the triplet (2m, m²−1, m²+1) is Pythagorean. When m = 2, we get (4, 3, 5); when m = 3, we get (6, 8, 10); when m = 4, we get (8, 15, 17); when m = 5, we get (10, 24, 26). This formula does not generate all Pythagorean triplets — for example (5, 12, 13) requires a different generating approach — but it produces an infinite family. Students must verify triplets by calculating: does a² + b² equal c²? For (8, 15, 17): 8² + 15² = 64 + 225 = 289 = 17². Pythagorean triplets connect to Class 9 Triangles chapter and Class 10 Coordinate Geometry. In CBSE exams, 1-2 marks typically test either verification or generation of triplets. The concept also appears in Olympiad problems involving right triangles with integer sides.

Square Root by Prime Factorisation Method

The prime factorisation method for finding square roots is the first technique taught in CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots. This method works efficiently for perfect squares where complete pairing of prime factors is possible. Step 1: Express the number as a product of prime factors using repeated division. Step 2: Group the prime factors into identical pairs. Step 3: Take one factor from each pair and multiply them to get the square root. If any prime factor is left unpaired, the number is not a perfect square. For finding the smallest multiplier or divisor to make a number a perfect square, identify unpaired primes: if a prime appears an odd number of times, either multiply by that prime once (to complete the pair) or divide by that prime once (to remove the unpaired factor). NCERT Exercise 5.3 contains 10 questions applying this method to numbers like 729, 1764, 4096, 9216, and five-digit numbers like 17424. This method is faster than long division for perfect squares up to four digits and helps students understand the fundamental theorem of arithmetic.

Long Division Method for Square Roots — The Complete Algorithm

The long division method is the signature technique of CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots, appearing in 4-5 marks worth of questions in board exams. Unlike prime factorisation, this method works for both perfect and non-perfect squares and can compute square roots to any required decimal place. The algorithm: Step 1 — Place a bar over every pair of digits starting from the units place (for decimal numbers, pair digits on both sides of the decimal point). Step 2 — Find the largest number whose square is less than or equal to the first pair or single digit; this becomes the first digit of the answer. Step 3 — Subtract this square from the first pair and bring down the next pair of digits. Step 4 — Double the current quotient and write it as the new divisor with a blank digit to its right. Step 5 — Determine the largest digit for the blank that, when placed and multiplied by the complete divisor, does not exceed the current dividend. Step 6 — Repeat steps 3-5 until all digit pairs are exhausted. For decimals, continue pairing zeros to achieve desired precision. Students typically need to solve 15-20 problems to master this method, as the carry-over logic differs from standard long division.
  • For perfect squares, the division ends with remainder zero; for non-perfect squares, continue adding pairs of zeros after the decimal point
  • When finding √2 to three decimal places, pair as (2.00 00 00) and continue the algorithm for three iterations past the decimal
  • Common error: forgetting to double the quotient at each step — the divisor pattern is not obvious and requires careful attention
  • The method appears identical in CBSE Class 10 for simplifying surds and in Class 11 for numerical methods

Worked Example — Finding √4096 by Long Division

Let us find the square root of 4096 using the long division method taught in CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots. Step 1: Place bars over pairs of digits from right to left: 40'96. Step 2: The largest number whose square ≤ 40 is 6 (since 6² = 36 and 7² = 49). Write 6 as the first digit of the answer. Subtract 36 from 40, getting remainder 4. Bring down the next pair 96 to make 496. Step 3: Double the current quotient 6 to get 12. Our divisor now looks like '12_' where the blank is a digit d. We need 12d × d ≤ 496. Testing: 124 × 4 = 496 exactly. So the next digit is 4. Step 4: Subtract 496 from 496 to get remainder 0. Since no pairs remain and remainder is zero, 4096 is a perfect square with √4096 = 64. The verification: 64² = 4096 confirms our answer. This example illustrates the perfect pairing that occurs with perfect squares. When working with non-perfect squares like 5300, the division would continue with pairs of zeros (53'00.00'00...) to compute decimal approximations.

Common Mistakes Students Make in CBSE Class 8 Mathematics Chapter 5

After reviewing thousands of CBSE Class 8 answer sheets, five recurring errors appear in CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots problems. Error 1: Confusing square and square root — writing 5² = 25 and then incorrectly stating √25 = 5² instead of √25 = 5. Error 2: In prime factorisation, failing to pair all instances of a prime before concluding a number is not a perfect square. For 1800 = 2³ × 3² × 5², students often take √1800 = 2 × 3 × 5 = 30, forgetting that 2³ has an unpaired 2. Error 3: In long division, forgetting to double the quotient at each step. Students repeat the previous divisor instead of updating it, leading to wrong digits. Error 4: When finding the smallest multiplier to make a number a perfect square, students multiply by the entire unpaired prime factor rather than just one instance. If 2³ appears, multiply by 2¹, not 2³. Error 5: Misreading the bar placement in long division — pairing from left to right instead of right to left, which shifts all subsequent calculations. Teachers recommend colour-coding the bars during practice to avoid this error. Addressing these through worked examples reduces average error rates from 40% to under 15%.
  • Use different colours for paired and unpaired factors in prime factorisation to visually separate them
  • Write the doubling step explicitly: 'Current quotient = 6, so new divisor starts with 12'
  • Always verify your square root answer by squaring it and checking against the original number
  • When estimating square roots, use nearest perfect squares as bounds: √50 is between √49=7 and √64=8, closer to 7

Relationship Between Squares, Square Roots, and Area Calculations

CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots builds the bridge between arithmetic and geometry through area problems. Since the area of a square with side s is s², finding the side length when area is known requires computing the square root. A square garden of area 2025 m² has side length √2025 = 45 m. When a square plot of 1024 m² is divided into four equal squares, each smaller square has area 256 m² and side √256 = 16 m. The chapter includes several NCERT problems where students must find the number of slabs required to tile a square floor, involving both area calculation and square root extraction. Word problems also explore scenarios like: 'A farmer has 8281 plants and wants to arrange them in a square grid — how many rows and columns?' Answer: √8281 = 91, so a 91×91 arrangement. These applications reappear in Class 9 Chapter 12 Heron's Formula and Class 10 Chapter 5 Arithmetic Progressions, making mastery essential. Approximately 2-3 marks in CBSE Class 8 final exams come from such application problems.

Exam Pattern and Marking Scheme for Squares and Square Roots

In the CBSE Class 8 final examination, CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots typically carries 8-10 marks distributed across three question types. One 1-mark question tests properties: 'Which of the following cannot be a perfect square?' or 'Find the smallest number to be multiplied with 1800 to make it a perfect square.' Two 2-mark questions require either prime factorisation square root calculation or identification of Pythagorean triplets with verification. One 3-mark question presents a long division square root problem, often for a four-digit perfect square or a three-decimal-place approximation of a non-perfect square. One 4-mark word problem integrates square roots with area, requiring multi-step reasoning. Sample question: 'A rectangular field of length 40 m and breadth 22.5 m is to be converted into a square field of equal area. Find the side of the square field and the cost of fencing at ₹15 per metre.' The 2024-25 CBSE sample paper included a 3-mark question on finding √17.64 by long division. Internal assessments and periodic tests usually allocate 5 marks from this chapter in a 40-mark paper. Students should budget 12-15 minutes for CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots questions in a 3-hour paper.

How CBSETUTOR.ai Helps Master CBSE Class 8 Mathematics Chapter 5

Parents across India report that CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots, particularly the long division method, creates a confidence gap because schools often rush through the algorithm in 2-3 periods without adequate individual practice. CBSETUTOR.ai addresses this through its 24×7 AI tutor trained on every page of the NCERT Class 8 Mathematics textbook. A student can photograph any problem from Exercise 5.3 or 5.4, upload it to the platform, and receive a step-by-step worked solution with the exact doubling logic and divisor formation explained at each stage. The AI recognises handwritten work, identifies where the student's calculation diverged from the correct algorithm, and provides targeted correction. For conceptual questions like 'Why can a number ending in 3 never be a perfect square?', the tutor delivers an NCERT-aligned explanation with counterexamples. Unlike pre-recorded videos that cannot adapt to individual confusion points, CBSETUTOR.ai lets the student ask follow-up questions in natural language: 'Why did we double the quotient here?' or 'How do I know which digit to try next?' At ₹999 per month flat for access to Class 6-12 content across all subjects, with a 3-day free trial requiring no credit card, parents find this more effective than ₹5000-8000 monthly tuition fees, especially for chapters requiring extensive practice like Squares and Square Roots.
  • Upload photos of NCERT Exercise 5.4 long division problems and receive annotated step-by-step solutions showing each divisor doubling
  • Ask 'How do I find the smallest multiplier for 2888 to become a perfect square?' and get the prime factorisation worked out with pairing logic
  • Practice unlimited auto-generated problems on square root estimation, Pythagorean triplet verification, and property identification
  • Access the platform 24×7 from any device, making it ideal for last-minute doubt clearing before Class 8 exams or periodic tests

Preparation Strategy for CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots

A systematic 10-day preparation plan ensures mastery of CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots. Days 1-2: Read NCERT pages on properties of square numbers and solve Exercise 5.1 completely, making a flashcard list of all seven properties. Days 3-4: Understand Pythagorean triplets, generate triplets for m = 2 through m = 10, verify each, and solve Exercise 5.2. Days 5-6: Master prime factorisation method by solving all 10 questions of Exercise 5.3 twice — once with teacher/tutor help, once independently. Days 7-8: Learn the long division algorithm through 5 worked examples before attempting Exercise 5.4; work through 3 perfect square examples and 2 non-perfect square decimal approximations. Days 9: Solve all word problems in the chapter and attempt 5 additional problems from RD Sharma or RS Aggarwal for extra practice. Day 10: Take a full-chapter mock test under timed conditions (25 minutes for 10 marks), identify weak areas, and revise those topics. Students should maintain a separate notebook for CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots with solved examples, common errors, and quick reference formulas. Revise properties and Pythagorean triplet formula daily for 5 minutes during the preparation period.
  • Solve at least 20 long division problems manually without calculator to build muscle memory for the algorithm
  • Create error logs: note down each mistake, its correct solution, and the conceptual gap that caused it
  • Use estimation to verify answers: √4800 should be close to √4900 = 70, so an answer of 69.28 is reasonable while 120 is not
  • Form study groups to quiz each other on properties and verify each other's long division working step-by-step

Connecting Class 8 Squares and Square Roots to Higher Classes

CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots is not a standalone topic but the foundation for multiple chapters across Classes 9-12. In Class 9, Chapter 1 on Real Numbers revisits square roots in the context of rational and irrational numbers — students learn that √2, √3, √5 are irrational and prove this using properties learned in Class 8. Class 9 Chapter 12 Heron's Formula requires computing square roots of large numbers to find triangle areas using √(s(s−a)(s−b)(s−c)). In Class 10, Chapter 4 Quadratic Equations depends entirely on square root extraction: solving x² − 5x + 6 = 0 via factorisation or using the quadratic formula (−b ± √(b²−4ac))/(2a) both require fluent square root calculation. Class 10 Chapter 6 on Triangles uses Pythagoras theorem (a² + b² = c²) extensively, making Pythagorean triplets from Class 8 directly applicable. In Class 11, Chapter 5 Complex Numbers introduces √(−1) = i, extending the square root concept to imaginary numbers. The long division method taught in CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots reappears in Class 11 numerical methods for approximating roots of equations. Students who master this chapter in Class 8 report 25-30% faster problem-solving in Class 10 board exams.

Additional Resources and Practice for CBSE Class 8 Mathematics Chapter 5

Beyond the NCERT textbook, students preparing for CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots should use supplementary resources strategically. The NCERT Exemplar for Class 8 Mathematics contains 15 additional challenging problems on this chapter, including multi-step word problems and proof-based questions ideal for Olympiad preparation. RD Sharma Class 8 Mathematics has 40+ graded exercises on squares and square roots, progressing from basic to advanced. RS Aggarwal Class 8 includes 10 solved examples and 35 practice problems with step-by-step solutions. For visual learners, DIKSHA platform (by NCERT) provides QR code-linked animated explanations of the long division method. Past years' CBSE Class 8 question papers (2020-2024) available on the official CBSE website show recurring question patterns: smallest multiplier problems appear almost every year, and one long division 3-mark question is standard. State board question banks from Kerala, Tamil Nadu, and Karnataka offer additional practice since all follow similar NCERT curricula. Students targeting NTSE or Math Olympiads should solve the square and square root section from previous years' Stage 1 papers, which feature advanced property-based reasoning questions.
  • NCERT Exemplar problems 5.1 to 5.15 for competition-level practice beyond board exam requirements
  • DIKSHA app QR codes from NCERT Class 8 textbook pages 110-125 for animated step-by-step explanations
  • Previous 5 years' CBSE sample papers (2020-2024) for pattern analysis and repeated question types
  • Math Olympiad archives from AMTI and PRMO for property-based reasoning and proof questions involving squares

Frequently asked questions

How many marks does CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots carry in the final exam?+
CBSE Class 8 Mathematics Chapter 5 typically carries 8-10 marks in the final 80-mark examination. The marks distribute as: one 1-mark property question, two 2-mark calculation problems, one 3-mark long division question, and one 4-mark application word problem involving area or practical situations.
Is the long division method for square roots still necessary when calculators are allowed in higher classes?+
Yes, absolutely. CBSE Class 10 board exams prohibit calculators, and many problems require showing the complete working for square root extraction to earn full marks. Moreover, Class 11-12 numerical methods and approximation techniques build directly on the long division algorithm. Understanding the method develops number sense that calculator dependence erodes.
My child understands prime factorisation but struggles with long division for square roots — what is the best practice approach?+
Start with perfect two-digit squares (√64, √81, √49) to build confidence with the algorithm structure without complex arithmetic. Then move to perfect three-digit squares (√144, √225, √289). Use graph paper to maintain neat columns, which helps track the doubling steps visually. Solve 5 problems daily for one week rather than 20 in one sitting. CBSETUTOR.ai's step-by-step photo-based solutions show exactly where the working goes wrong when a student uploads their attempt.
What is the fastest way to identify whether a large number is a perfect square without calculating?+
Check the units digit first: if it is 2, 3, 7, or 8, immediately reject it as not a perfect square. If it ends in 0, count zeros — an odd number means not a perfect square. For remaining cases, perform quick prime factorisation: if any prime appears an odd number of times, it is not a perfect square. This elimination process takes under 30 seconds and prevents wasting time on full calculations.
How do Pythagorean triplets from Class 8 help in Class 10 board exams?+
Class 10 Chapter 6 Triangles extensively uses Pythagoras theorem. Recognising standard triplets like (3,4,5), (5,12,13), (8,15,17), and (7,24,25) allows instant identification of right triangles without calculation. In 3-mark geometry problems, this saves 2-3 minutes. Additionally, coordinate geometry problems asking for distance often yield these triplet values, providing a quick accuracy check.
Can CBSETUTOR.ai help if my child's school uses a different reference book instead of NCERT?+
Yes. CBSETUTOR.ai is trained on the complete NCERT syllabus which forms the core of all CBSE examinations regardless of school textbook. Students can photograph problems from any book — RD Sharma, RS Aggarwal, Pearson, or school worksheets — and receive solutions aligned with NCERT terminology and CBSE marking schemes. The final exam tests NCERT content, so CBSETUTOR.ai's NCERT-grounded explanations ensure no gaps.
What are the most common errors students make in CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots that cost marks in exams?+
Five errors cost the most marks: (1) writing √25 = 5² instead of √25 = 5 — confusing square and square root notation; (2) in prime factorisation, forgetting that all exponents must be even for a perfect square; (3) in long division, failing to double the quotient at each step; (4) misplacing bars over digit pairs, pairing from left instead of right; (5) not verifying the final answer by squaring it back. Each error typically costs 1-2 marks in a 3-4 mark problem.
How much time should a Class 8 student spend daily on Squares and Square Roots during the preparation phase?+
During active learning (when the chapter is being taught), allocate 30-40 minutes daily: 10 minutes reviewing concepts, 25 minutes solving 4-5 NCERT problems, and 5 minutes noting down errors. During revision phase before exams, spend 20 minutes daily for one week: solve one complete exercise under timed conditions, check answers, and revise properties. Consistent daily practice is more effective than weekend marathon sessions for this calculation-intensive chapter.
Does CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots appear in competitive exams like NTSE and Olympiads?+
Yes, extensively. NTSE Stage 1 typically includes 2-3 questions on properties of perfect squares, often requiring multi-step reasoning ('Find the smallest perfect square divisible by 6, 8, and 12'). Math Olympiads (PRMO, RMO) feature advanced problems involving digit patterns in squares and proofs about square number properties. Mastering CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots at a deep conceptual level provides significant advantage in these competitions.
What is the generating formula for Pythagorean triplets and does it produce all possible triplets?+
The NCERT formula (2m, m²−1, m²+1) for any natural number m > 1 generates an infinite family of Pythagorean triplets. However, it does not produce all triplets — for example, (5,12,13) and (20,21,29) cannot be generated by this formula. The complete parameterisation (m²−n², 2mn, m²+n²) for coprime integers m > n generates all primitive Pythagorean triplets, but this is beyond CBSE Class 8 scope.
Why does the NCERT textbook teach square root by long division when prime factorisation is simpler?+
Prime factorisation only works for perfect squares with factorisable numbers. Long division extends to non-perfect squares (√7, √20), large numbers where factorisation is tedious, and decimal approximation to any required precision. Additionally, the long division algorithm teaches place-value reasoning and systematic problem decomposition valuable across mathematics. It remains the only manual method for computing √2 ≈ 1.414 or √7 ≈ 2.646 to specified accuracy.
If my child is weak in multiplication tables, will that severely affect performance in CBSE Class 8 Mathematics Chapter 5 Squares and Square Roots?+
Yes, significantly. Both prime factorisation and long division require instant recall of multiplication facts up to 20×20 and recognition of perfect squares up to 20² = 400. A child struggling with tables will spend 3-4× longer on each problem and make more arithmetic errors. Strengthen tables first using daily 10-minute drills for two weeks before attempting this chapter. CBSETUOR.ai can generate unlimited table practice problems and instant checking.

Related resources

Important Questions: CBSE Class 8 Mathematics Chapter 5 Squares and Square RootsClass 8 Mathematics Chapter 5 Squares and Square Roots — Formulas & Key PointsCBSE Class 8 Mathematics Chapter 5 Squares and Square Roots Worksheet with Answersमहत्वपूर्ण प्रश्न: CBSE कक्षा 8 गणित अध्याय 5 वर्ग और वर्गमूलAI Tutor for Class 8: The Smart Alternative to TuitionAI Tutor for Class 8 Science: Learn Faster with Instant HelpNCERT Solutions for Class 9 Mathematics Chapter 2: PolynomialsCBSE Class 9 Mathematics — Number Systems: complete chapter guide

Keep learning — related guides

Class 8Mathematics
CBSE Class 8 Mathematics Chapter 13 Introduction to Graphs: Mind Map & Revision Notes
Class 8Mathematics
CBSE Class 8 Mathematics — Introduction to Graphs: complete chapter guide
Class 8Mathematics
CBSE Class 8 Mathematics Chapter 13 Introduction to Graphs — Notes
Class 8Mathematics
NCERT Solutions for CBSE Class 8 Mathematics Chapter 13: Introduction to Graphs
Class 8Mathematics
CBSE Class 8 Mathematics Chapter 12 Factorisation: mind map & revision
Class 8Mathematics
CBSE Class 8 Mathematics — Factorisation: complete chapter guide

Ready to give your Class 8 child the tutor that never sleeps?

CBSETUTOR.ai covers every chapter in the Class 8 NCERT syllabus — Maths, Science, Social Science, English, Hindi and more. 24×7. Patient. Unlimited. 3-day free trial.

Start your child's 3-day free trial →