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Simplify: \(\left ( \sqrt3 -\dfrac{1}{\sqrt3} \right )^2\)

  • A.\(\dfrac{3}{4}\)
  • B.\(\dfrac{4}{\sqrt 3}\)
  • C.\(\dfrac{4}{3}\)
  • D.None of these

Answer: C

\(\left ( \sqrt3 -\dfrac{1}{\sqrt3} \right )^2\\ =\left ( \sqrt 3 \right )^2 + \left ( \dfrac{1}{\sqrt3} \right )^2 -2 \times \sqrt 3 \times \dfrac{1}{\sqrt3}\\ = 3 + \dfrac{1}{3} - 2\\ =1 + \dfrac{1}{3}\\ =\dfrac{4}{3}\)

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