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Simplify: 3+22−3−22\sqrt{3 + 2\sqrt{2}} - \sqrt{3 - 2\sqrt{2}}.

  1. 22

  2. 222\sqrt{2}

  3. 2\sqrt{2}

  4. 44

Show answer & explanation

Correct answer

22

Explanation

Let x=3+22−3−22x = \sqrt{3+2\sqrt{2}} - \sqrt{3-2\sqrt{2}}. Squaring: x2=3+22+3−22−2(3)2−(22)2=6−29−8=6−2=4x^2 = 3+2\sqrt{2} + 3-2\sqrt{2} - 2\sqrt{(3)^2 - (2\sqrt{2})^2} = 6 - 2\sqrt{9-8} = 6 - 2 = 4. So x=2x=2 (positive).

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