Question

Simplification of ${(\sqrt{3}-\frac{1}{\sqrt{3}})}^2$ is

• A. $\frac{4}{3}$
• B. $\frac{4}{\sqrt{3}}$
• C. $4$
• D. $Noneofthese$

Answer 1

The correct option is A $\frac{4}{3}$

${(\sqrt{3}-\frac{1}{\sqrt{3}})}^2$

$[\therefore (a-b{)}^2=a^2-2ab+b^2]$

${(\sqrt{3}-\frac{1}{\sqrt{3}})}^2=(\sqrt{3}{)}^2-2(\sqrt{3})\left(\frac{1}{\sqrt{3}}\right)+{\left(\frac{1}{\sqrt{3}}\right)}^2$

$=3-2\left(1\right)+\frac{1}{3}$

$=\frac{9-6+1}{3}$

$=\frac{4}{3}$