Question

The square root of $39$ lies between which two natural numbers?

• A. $38$ and $40$
• B. $5$ and $6$
• C. $6$ and $7$
• D. $7$ and $8$

Answer 1

The correct option is C $6$ and $7$

As we know that $36$ is the square of $6$.
$6^2=36$
$\Rightarrow \sqrt{36}=6$

Also, $49$ is the square of $7$.
$7^2=49$
$\Rightarrow \sqrt{49}=7$

The nearest two perfect square numbers of $39$ are $36$ and $49$, hence
$36<39<49$
$\Rightarrow \sqrt{36}<\sqrt{39}<\sqrt{49}$
$\Rightarrow 6<\sqrt{39}<7$
$(\because \text{we got}\sqrt{36}=6\text{and}\sqrt{49}=7)$

From the above expression, it is clear that the square root of $39$ would lie between $6$ and $7$.

Therefore, option (c.) is the correct answer.