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Question

\(\left({\sqrt{3}-\frac{1}{\sqrt{3}}}\right)^{2}\)  simplifies to :

Options:
A .  \(\frac{3}{4}\)
B .  \(\frac{4}{\sqrt{3}}\)
C .  \(\frac{4}{3}\)
D .  None of these
Answer: Option C

\((\sqrt{3}-\frac{1}{\sqrt{3}})^{2} = (\sqrt{3})^{2}+(\frac{1}{\sqrt{3}})^{2}-2\times\sqrt{3}\times\frac{1}{\sqrt{3}}\)


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


\(= 1+\frac{1}{3}\)


\(= \frac{4}{3}\)


 


 


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