Question

Which of the following is not an irrational number?

• A. $5-\sqrt{3}$
• B. $5+\sqrt{3}$
• C. $4+\sqrt{2}$
• D. $5+\sqrt{9}$

Answer 1

The correct option is D

$5+\sqrt{9}$

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.