Question

Choose the irrational number that lies between 5 and 9.

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

Answer 1

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

$6\times 6$ = 36, a perfect square, hence $\sqrt{36}$ is not irrational.
Also 25 is the perfect square of 5, hence $\sqrt{25}$ is rational.

$5^2=25$ and $9^2=81$, hence all the numbers between $\sqrt{25}$ and $\sqrt{81}$ lie between 5 and 9.

We can see that only irrational $\sqrt{31}$ lies between $\sqrt{25}$ and $\sqrt{81}$, that is it lies between 5 and 9.

$\sqrt{17}$ is an irrational number but it is less than 5.