Question

Identify the integer(s) whose square root lies between $2$ and $3.$

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

Answer: (A), (B), (C), (D)

$8$

Let the required integer be $m$
Given: $2<\sqrt{m}<3$

On squaring both sides of the inequality, we get:
$\Rightarrow 4<m<9$

The integers which lie between $4$ and $9$ are $5,6,7$ and $8.$

Apply the perfect square method.

Let's take $7$ as an example.

$4<7<9$
(taking square root throughout the inequality)
$\Rightarrow \sqrt{4}<\sqrt{7}<\sqrt{9}$
$\Rightarrow 2<\sqrt{7}<3$

$\therefore \sqrt{7}$ lies between $2$ and $3.$
Similarly, $\sqrt{5},\sqrt{6}$ and $\sqrt{8}$ lies between $2$ and $3.$