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SSC CGL 2025 PYQ — Question 75

SSC CGL - 19 Sep 2025 - Shift 1 • Quantitative Aptitude • Q75

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Simplify the expression: (9+45)\sqrt{(9+4\sqrt5)}

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 5+2\sqrt5+2.

(9+45)\sqrt{(9+4\sqrt5)}

=(5+4+45)=\sqrt{(5+4+4\sqrt5)}

=[(5)2+22+2×5×2]=\sqrt{[(\sqrt5)^2+2^2+2\times\sqrt5\times2]}

=(5+2)2=\sqrt{(\sqrt5+2)^2}

=5+2=\sqrt5+2