Class 8 · Chapter 6

Squares and Square Roots

Perfect squares; finding square roots by prime factorisation and long division.

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Tip: open the NCERT PDF for the original chapter text alongside the notes here.

Detailed theory

Number whose square root is a natural number:

1, 4, 9, 16, 25, \ldots

. Ends in

0, 1, 4, 5, 6, 9

only.

Key concepts & formulas

A perfect square ends in

0,1,4,5,6,9

in the units place.

Product of two consecutive numbers cannot be a perfect square.

Pair the primes to find

\sqrt{n}

(a+b)^2 = a^2 + 2ab + b^2

For any perfect square, its square root has half the digits (rounded up).