Which of the following is not an irrational number?

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Question

Which of the following is not an irrational number?

Options:

A .

5 - \sqrt{3}

B .

5 + \sqrt{3}

C .

4 + \sqrt{2}

D .

5 + \sqrt{9}

Answer: Option D
:
D

If p is a prime number, then $\sqrt{p}$ is an irrational number.
3 is a prime number.
$\Rightarrow$ $\sqrt{3}$ is an irrational number.
$\Rightarrow$ $5 - \sqrt{3}$ is an irrational number.
Similarly, $5 + \sqrt{3}$ is an irrational number.
2 is a prime number.
$\Rightarrow$ $\sqrt{2}$ is an irrational number.
$\Rightarrow$ $4 + \sqrt{2}$ is an irrational number.
9 is not a prime number.
$\sqrt{9} = 3$
$\Rightarrow$ $5 + \sqrt{9} = 5 + 3 = 8$ which is a rational number.
$\Rightarrow$ $5 + \sqrt{9}$ is not an irrational number.

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