Question
$${\left( {\sqrt 3 - \frac{1}{{\sqrt 3 }}} \right)^2}$$ simplifies to ?
Answer: Option C
$$\eqalign{
& = {\left( {\sqrt 3 - \frac{1}{{\sqrt 3 }}} \right)^2} \cr
& = {\left( {\sqrt 3 } \right)^2} + {\left( {\frac{1}{{\sqrt 3 }}} \right)^2} - 2 \times \sqrt 3 \times \frac{1}{{\sqrt 3 }} \cr
& = 3 + \frac{1}{3} - 2 \cr
& = 1 + \frac{1}{3} \cr
& = \frac{4}{3} \cr} $$
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$$\eqalign{
& = {\left( {\sqrt 3 - \frac{1}{{\sqrt 3 }}} \right)^2} \cr
& = {\left( {\sqrt 3 } \right)^2} + {\left( {\frac{1}{{\sqrt 3 }}} \right)^2} - 2 \times \sqrt 3 \times \frac{1}{{\sqrt 3 }} \cr
& = 3 + \frac{1}{3} - 2 \cr
& = 1 + \frac{1}{3} \cr
& = \frac{4}{3} \cr} $$
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