Question

From the options, choose the irrational numbers that lie between 4 and 9.

• A. $\sqrt{36}$
• B. $\sqrt{31}$
• C. $\sqrt{17}$
• D. $\sqrt{25}$

Answer 1

Answer: (B), (C)

The correct options are
B

$\sqrt{31}$

C

$\sqrt{17}$

$6\times 6$ = 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 all the numbers between $\sqrt{16}$ and $\sqrt{81}$ lie between 4 and 9.

We can see that $\sqrt{17}$, $\sqrt{31}$ are irrational numbers between $\sqrt{16}$ and $\sqrt{81}$, and they lie between 4 and 9.