Question

Which of the following irrational numbers lie between $6$ and $8$?

• A. $\sqrt{49}$
• B. $\sqrt{19}$
• C. $\sqrt{47}$
• D. $\sqrt{62}$

Answer 1

Answer: (C), (D)

$\sqrt{47}$
$\sqrt{62}$

We know, $6^2=36$, $7^2=49$ and $8^2=64$.

That is we have to find a value $\sqrt{x}$ such that $\sqrt{36}<\sqrt{x}<\sqrt{64}$ $⟹$ $6<\sqrt{x}<8$ .

From the list, the values that satisfies this condition are $\sqrt{49}$, $\sqrt{47}$ and $\sqrt{62}$.

From this, $\sqrt{49}=7$ is a rational number.

But $\sqrt{47}$ and $\sqrt{62}$ are irrational number.

That is, $\Rightarrow \sqrt{4}7$ and $\sqrt{6}2$ are only irrational numbers from the stated that lie in between $6$ and $8$.

Hence, option $C$ and $D$ are correct.