Question

State whether the following statement is TRUE or FALSE.

$(2-\sqrt{3}{)}^2$ is irrational.

• A. True
• B. False

Answer 1

The correct option is A True

Formula
${(a-b)}^2=a^2+b^2-2ab$

Applying the formula, we get
${(2-\sqrt{3})}^2=2^2+{\sqrt{3}}^2-2\times 2\times \sqrt{3}=4+3-4\sqrt{3}=7-4\sqrt{3}$

$7-4\sqrt{3}$ is an irrational number.

$⟹{(2-\sqrt{3})}^2$ is an irrational number.