NCERT Solutions Class 8 Maths Ganita Prakash Chapter 1 — A Square and A Cube#

Chapter 1 of Ganita Prakash Part I is about squares and cubes of numbers: which numbers are perfect squares or perfect cubes, how to find square roots and cube roots by prime factorisation, and how to estimate them.

Exercises#

• Figure it Out — Page 10 — Perfect squares, last digits, square roots by prime factorisation, numbers between squares, a square pattern (9 questions)
• Figure it Out — Page 16 — Cube roots, making a perfect cube, true or false about cubes, guessing cube roots (5 questions)

What you will learn#

• A perfect square ends in 0, 1, 4, 5, 6 or 9, and has an even number of zeros at the end.
• A number is a perfect square when its prime factors split into two identical groups, and a perfect cube when they split into three.
• There are $2n$ numbers between $n^2$ and $(n + 1)^2$.
• Estimating a square root between two perfect squares.

Key formulas and results#

• $(n + 1)^2 = n^2 + 2n + 1$
• $\sqrt{a^2 \times b^2} = a \times b$ and $\sqrt[3]{a^3 \times b^3} = a \times b$
• The last digit of a cube decides the last digit of its cube root: 0→0, 1→1, 8→2, 7→3, 4→4, 5→5, 6→6, 3→7, 2→8, 9→9.

Read and revise#

• NCERT Class 8 Maths Chapter 1 (PDF) — the Ganita Prakash Part I chapter itself.
• All Class 8 Maths chapters from Ganita Prakash Part I and Part II.

Frequently asked questions#