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2 / 20SimplificationEasyQuantitative Aptitude

Find the value of 17+122+17−122\sqrt{17 + 12\sqrt{2}} + \sqrt{17 - 12\sqrt{2}}.

  1. 66

  2. 88

  3. 44

  4. 2172\sqrt{17}

Show answer & explanation

Correct answer

66

Explanation

Let x=17+122+17−122x = \sqrt{17 + 12\sqrt{2}} + \sqrt{17 - 12\sqrt{2}}. Squaring: x2=17+122+17−122+2(17)2−(122)2=34+2289−288=34+2=36x^2 = 17 + 12\sqrt{2} + 17 - 12\sqrt{2} + 2\sqrt{(17)^2 - (12\sqrt{2})^2} = 34 + 2\sqrt{289 - 288} = 34 + 2 = 36. So x=6x=6 (positive).

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