Exams › SSC CGL (Prelims) › General

Simplify the expression: \(\sqrt{14 + 6\sqrt5}\).

1. 2 + \sqrt 5
2. 5 + \sqrt 3
3. 3 + \sqrt 5
4. 4 + \sqrt 2

Correct answer: 3 + \sqrt 5

Solution

Write \(\sqrt{14+6\sqrt5}\) as \(\sqrt x + \sqrt y\). Then \(x+y=14\) and \(2\sqrt{xy}=6\sqrt5\), so \(xy=45\). The numbers are 9 and 5, giving \(\sqrt9+\sqrt5=3+\sqrt5\).

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