Question

From the options, choose the irrational number(s) that lie between 4 & 9.

• A. √36
• B. √31
• C. 7
• D. √25

Answer 1

Answer: (B), (C)

The correct options are
B

√31

C

7

$4\times 9$ = 36, a perfect square, hence $\sqrt{36}$ is not irrational .
Also 25 is the perfect square of 5, hence $\sqrt{25}$ is rational

$4^2=16$ & $9^2=81$, hence numbers in between $\sqrt{16}$ & $\sqrt{81}$ lie between 4 & 9.

Hence $\sqrt{17}$,$\sqrt{31}$ etc. are irrational numbers between $\sqrt{16}$ & $\sqrt{81}$. So, they lie between 4 & 9.