Question

If $\sqrt{3}$ is an irrational number, then which of the following is an irrational number?

• A. $\sqrt{3}-\sqrt{3}$
• B. $\sqrt{3}(2\sqrt{3}-\sqrt{3})$
• C. $(\sqrt{3}-1)(\sqrt{3}+1)$
• D. $\sqrt{3}(\sqrt{3}-1)$

Answer 1

The correct option is D $\sqrt{3}(\sqrt{3}-1)$

$\sqrt{3}-\sqrt{3}=0\to$ rational number
$\sqrt{3}(2\sqrt{3}-\sqrt{3})=6-3=3\to$ rational number
$(\sqrt{3}+1)(\sqrt{3}+1)=3-1=2\to$ rational number
$\sqrt{3}(\sqrt{3}-1)=3-\sqrt{3}\to$ irrational number
(Sum/difference of a rational number and an irrational number is irrational.)