(√(3)-1/(√(3)))² simplifies to · ABC26GN1410
Subject: General Aptitude · Chapter: Square Roots and Cube Roots
$\left(\sqrt{3}-\frac{1}{\sqrt{3}}\right)^{2}$ simplifies to
(a)$\frac{3}{4}$
(b)$\frac{4}{\sqrt{3}}$
(c)$\frac{4}{3}$
(d)None of these
Answer
Explanation
$$\begin{aligned} \left(\sqrt{3}-\frac{1}{\sqrt{3}}\right)^{2} & =(\sqrt{3})^{2}+\left(\frac{1}{\sqrt{3}}\right)^{2}-2 \times \sqrt{3} \times \frac{1}{\sqrt{3}} \\ & =3+\frac{1}{3}-2=1+\frac{1}{3}=\frac{4}{3} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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