Question

Find the square root of the following numbers by the factorization method:
(i) $729$ (ii) $400$
(iii) $1764$ (iv) $4096$
(v) $7744$ (vi) $9604$
(vii) $5929$ (viii) $9216$
(ix) $529$ (x) $8100$

Answer 1

(i) $\sqrt{729}=\sqrt{(3\ast 3\ast 3\ast 3\ast 3\ast 3)}$

= 3 * 3 * 3

= 27
(ii)$\sqrt{400}=\sqrt{(2\ast 2\ast 2\ast 2\ast 5\ast 5)}$

= 2 * 2 * 5

= 20
(iii)$\sqrt{1764}=\sqrt{(2\ast 2\ast 3\ast 3\ast 7\ast 7)}$

= 2 * 3 * 7

= 42
(iv) $\sqrt{4096}=\sqrt{(2\ast 2\ast 2\ast 2\ast 2\ast 2\ast 2\ast 2\ast 2\ast 2)}$

= 2 * 2 * 2 * 2 * 2 * 2

= 64
(v) $\sqrt{7744}=\sqrt{(2\ast 2\ast 2\ast 2\ast 2\ast 2\ast 11\ast 11)}$

= 2 * 2 * 2 * 11

= 88
(vi) $\sqrt{9604}=\sqrt{(2\ast 2\ast 7\ast 7\ast 7\ast 7)}$

= 2 * 7 * 7

= 98
(vii) $\sqrt{5929}=\sqrt{(7\ast 7\ast 11\ast 11)}$

= 7 * 11

= 77

(viii) $\sqrt{9216}=\sqrt{(2\ast 2\ast 2\ast 2\ast 2\ast 2\ast 2\ast 2\ast 2\ast 2\ast 3\ast 3)}$

= 2 * 2 * 2 * 2 * 2 * 3

= 96

(ix) $\sqrt{529}=\sqrt{(23\ast 23)}$

= 23
(x)$\sqrt{8100}=\sqrt{(2\ast 2\ast 3\ast 3\ast 3\ast 3\ast 5\ast 5)}$

= 2 * 3 * 3 * 5

= 90