Question

Find the square roots of the following decimal numbers:
(i) $7.29$ (ii) $16.81$ (iii) $9.3025$ (iv) $84.8241$

Answer 1

(i) $7.29=\frac{729}{100}$

$=\sqrt{\frac{3\times 3\times 3\times 3\times 3\times 3}{10\times 10}}$

$=\frac{3\times 3\times 3}{10}$

$=2.7$

(ii) $16.81=\frac{1681}{100}$

$=\sqrt{\frac{41\times 41}{10\times 10}}$

$=4.1$

(iii) $9.3025=\frac{93025}{10000}$

$=\sqrt{\frac{5\times 5\times 61\times 61}{10\times 10\times 10\times 10}}$

$=3.05$

(iv) $84.8241=\frac{848241}{10000}$

$=\sqrt{\frac{3\times 3\times 307\times 307}{10\times 10\times 10\times 10}}$

$=9.21$