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Geometric mean of radical expressions

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

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The geometric mean proportion between 30+20030 + \sqrt{200} and 54−64854 - \sqrt{648} is:

  1. A.

    6\sqrt{2}

  2. B.

    4\sqrt{5}

  3. C.

    6\sqrt{35}

  4. D.

    5\sqrt{6}

Answer

C

Explanation

Simplify terms: 30+200=30+102=10(3+2)30 + \sqrt{200} = 30 + 10\sqrt{2} = 10(3 + \sqrt{2}). 54−648=54−182=18(3−2)54 - \sqrt{648} = 54 - 18\sqrt{2} = 18(3 - \sqrt{2}). Geometric mean GM=10(3+2)×18(3−2)=180×(32−(2)2)=180×7=1260=635GM = \sqrt{10(3 + \sqrt{2}) \times 18(3 - \sqrt{2})} = \sqrt{180 \times (3^2 - (\sqrt{2})^2)} = \sqrt{180 \times 7} = \sqrt{1260} = 6\sqrt{35}.

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