Question

Find the square root of the following decimal numbers
$\left(i\right)2.56$

$\left(ii\right)7.29$

$\left(iii\right)51.84$

$\left(iv\right)42.25$

$\left(v\right)31.36$

Answer 1

$256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=16\times 16$

(i) $\sqrt{2.56}=\sqrt{\frac{256}{100}}=\sqrt{\frac{16\times 16}{10\times 10}}=\frac{16}{10}=1.6$

$729=3\times 3\times 3\times 3\times 3\times 3=27\times 27$

(ii) $\sqrt{7.29}=\sqrt{\frac{729}{100}}=\sqrt{\frac{27\times 27}{10\times 10}}=\frac{27}{10}=2.7$

$5184=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\times 3=72\times 72$

(iii) $\sqrt{51.84}=\sqrt{\frac{5184}{100}}=\sqrt{\frac{72\times 72}{10\times 10}}=\frac{72}{10}=7.2$

$4225=5\times 5\times 13\times \times 13=65\times 65$

(iv) $\sqrt{42.25}=\sqrt{\frac{4225}{100}}=\sqrt{\frac{65\times 65}{10\times 10}}=\frac{65}{10}=6.5$

$3136=2\times 2\times 2\times 2\times 2\times 2\times 7\times 7=56\times 56$

(v) $\sqrt{31.36}=\sqrt{\frac{3136}{100}}=\sqrt{\frac{56\times 56}{10\times 10}}=\frac{56}{10}=5.6$