NCERT Class 8 Maths Chapter 1
A Square and a Cube
NCERT Class 8 Maths Chapter 1 (Ganita Prakash) introduces students to square numbers and cube numbers — their patterns, properties, and how to find square roots and cube roots. This CBSE chapter builds number sense by exploring why certain numbers are 'perfect' squares or cubes, using visual models and patterns. Students learn shortcut methods and real-world applications of these concepts.
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Key Terms
- Perfect Square
- A number that is the square of a whole number; e.g., 4 (=2²), 9 (=3²), 25 (=5²), 100 (=10²).
- Perfect Cube
- A number that is the cube of a whole number; e.g., 8 (=2³), 27 (=3³), 125 (=5³).
- Square Root
- The value which, when multiplied by itself, gives the original number; denoted by √; e.g., √25 = 5.
- Cube Root
- The value which, when multiplied by itself three times, gives the original number; denoted by ∛; e.g., ∛27 = 3.
- Prime Factorisation
- Expressing a number as a product of its prime factors; used to find square roots and cube roots.
- Pythagorean Triplet
- A set of three positive integers (a, b, c) satisfying a² + b² = c², such as (3, 4, 5) and (5, 12, 13).
- Exponent
- A number indicating how many times the base is multiplied by itself; in 5³, the exponent is 3 and the base is 5.
Frequently Asked Questions
What are square numbers Class 8 Maths?▾
Square numbers (perfect squares) are numbers obtained by multiplying a whole number by itself. For example: 1×1=1, 2×2=4, 3×3=9, 4×4=16, 5×5=25. These are called perfect squares. NCERT Class 8 Maths Chapter 1 explores patterns in square numbers and methods to find square roots.
How do you find the square root of a number Class 8 NCERT?▾
Two main methods are used in Class 8: (1) Prime Factorisation — factorise the number into primes, pair them up, and take one from each pair; e.g., √36 = √(2²×3²) = 2×3 = 6. (2) Long Division Method — used for large numbers. The prime factorisation method is most commonly tested in CBSE exams.
What are cube numbers Class 8?▾
Cube numbers are numbers obtained by multiplying a whole number by itself three times. For example: 1³=1, 2³=8, 3³=27, 4³=64, 5³=125. A perfect cube can be found by prime factorisation — if every prime factor appears in groups of three, the number is a perfect cube.
How do you find the cube root using prime factorisation Class 8?▾
To find the cube root using prime factorisation: (1) Write the prime factorisation of the number, (2) Group the prime factors into triplets, (3) Take one factor from each triplet and multiply them. Example: ∛216 = ∛(2³×3³) = 2×3 = 6.
What are Pythagorean triplets Class 8 Maths?▾
A Pythagorean triplet is a set of three positive integers (a, b, c) where a² + b² = c². Common examples are (3,4,5), (5,12,13), (8,15,17). To generate a triplet for any number m > 1: use (2m, m²-1, m²+1). For m=2: (4, 3, 5). These relate to right-angled triangles where c is the hypotenuse.
Is there a pattern in square numbers Class 8 NCERT?▾
Yes! Key patterns include: (1) Square numbers end only in 0, 1, 4, 5, 6, or 9 (never 2, 3, 7, or 8), (2) The difference between consecutive squares follows odd numbers: 4-1=3, 9-4=5, 16-9=7, (3) A number with odd number of zeros cannot be a perfect square, (4) The square of an odd number is odd; square of an even number is even.
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