Question

Write the prime factorization of the following numbers and hence find their square roots.
(i) 7744 (ii) 9604
(iii) 5929 (iv) 7056

Answer 1

Factorization, we get :
(i) 7744 = $2\times 2\times 2\times 2\times 2\times 2\times 11\times 11$

$\therefore$ Square root of 7744
=$\sqrt{7744}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 11\times 11}$
Grouping the factors in pairs of equal factors,
$\sqrt{7744}=2\times 2\times 2\times 2\times 7\times 7$
$\therefore$ Square root of 7744 = 88

(ii) $9604=2\times 2\times 2\times 2\times 7\times 7$

$\therefore$ Square root of 9604
$\sqrt{9604}=\sqrt{2\times 2\times 7\times 7\times 7\times 7}$
= $2\times 7\times =98$

(iii) $5929=7\times 7\times 11\times 11$

$\therefore$ Square root of 5929
=$\sqrt{5929}=\sqrt{7\times 7\times 11\times 11}$
= $7\times 11=77$

(iv) $7056=2\times 2\times 2\times 2\times 3\times 3\times 7\times 7$

$\therefore$ Square root of 7056
= $\sqrt{7056}=\sqrt{2\times 2\times 2\times 2\times 3\times 3\times 7\times 7}$
= $2\times 2\times 3\times 7=84$