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Rationalization of surd expression

CMAT 2018 · Quantitative Techniques & Data Interpretation · Easy · Algebra

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Find the value of 2+32−3\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}} correct to three places of decimal.

  1. A.

    3.141

  2. B.

    2.732

  3. C.

    3.124

  4. D.

    3.732

Answer

D

Explanation

Rationalizing the denominator: (2+3)(2+3)(2−3)(2+3)=(2+3)24−3=2+3=2+1.732=3.732.\sqrt{\frac{(2+\sqrt{3})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}} = \sqrt{\frac{(2+\sqrt{3})^2}{4-3}} = 2 + \sqrt{3} = 2 + 1.732 = 3.732.

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