Question

Which of the following is not a rational number?

• A. $\sqrt{2}$
• B. $\sqrt{4}$
• C. $\sqrt{9}$
• D. $\sqrt{16}$

Answer 1

Answer: (A)

$\sqrt{2}=\mathrm{1.4142135623730951....}$

$\sqrt{4}=\sqrt{2\times 2}=2$

$\sqrt{9}=\sqrt{3\times 3}=3$

$\sqrt{16}=\sqrt{4\times 4}=4$

As we can see the decimal representation of $\sqrt{2}$ is non-terminating non-repeating.

Hence, $\sqrt{2}$ is an irrational number.

Therefore, option $A$ is correct.