Question

The irrational numbers that lie between 4 and 9 is .

• A. $\sqrt{31}$
• B. $\sqrt{25}$
• C. $\sqrt{49}$
• D. $\sqrt{36}$

Answer 1

The correct option is A $\sqrt{31}$

$6\times 6$ = 36, a perfect square, hence $\sqrt{36}$ is not irrational .
Also 25 is the perfect square of 5, hence $\sqrt{25}$ is rational.
Simillarly, 49 is the perfect square of 7, hence $\sqrt{49}$ 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 $\sqrt{31}$ is the irrational number that lie between 4 and 9.