Question

Which of the following are two irrational numbers between 5 and 6 ?

• A. $\sqrt{25},\sqrt{36}$
• B. $\sqrt{5},\sqrt{6}$
• C. $\sqrt{5\sqrt{30}},\sqrt{30}$
• D. $5.5,5.7$

Answer 1

The correct option is C

$\sqrt{5\sqrt{30}},\sqrt{30}$

Since 5 and 6 are rational numbers and $5\times 6=30$ is not a perfect square.

$\therefore$ One irrational number between 5 and 6 is $\sqrt{5\times 6}=\sqrt{30}$

And, an irrational number between 5 and $\sqrt{30}=\sqrt{5\times \sqrt{30}}=\sqrt{5\sqrt{30}}$