Question

Find the approximate value of $\sqrt{30}$ using perfect square method.

• A. $4.47$
• B. $5.47$
• C. $6.47$

Answer 1

The correct option is B $5.47$

Using the perfect square method, the largest perfect square smaller than $30$ is $25.$
And the smallest perfect square greater than $30$ is $36.$

$25<30<36$
(taking square root throughout the inequality)
$\Rightarrow \sqrt{25}<\sqrt{30}<\sqrt{36}$
$\Rightarrow 5<\sqrt{30}<6$

$\therefore \sqrt{30}$ lies between $5$ and $6.$
From the given option, only $5.47$ satisfies this condition.
$\therefore$ Approximate value of $\sqrt{30}$ is $\mathrm{5.47.}$