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SSC CHSL 2025 PYQ — Question 72

SSC CHSL - 12 Nov 2025 - Shift 3 • Quantitative Aptitude • Q72

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Rationalize the denominator:47+5\frac{4}{\sqrt{7} + \sqrt{5}}

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Correct answer: B

Explanation

47+5\frac{4}{\sqrt{7} + \sqrt{5}}
By the formula:
(a+b)(a−b)=a2−b247+5×7−57−5=4(7−5)7−5=4(7−5)2=2(7−5)(a + b)(a - b) = a^2 - b^2 \\ \frac{4}{\sqrt{7} + \sqrt{5}} \times \frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} - \sqrt{5}} = \frac{4(\sqrt{7} - \sqrt{5})}{7 - 5} \\ = \frac{4(\sqrt{7} - \sqrt{5})}{2} \\ = 2(\sqrt{7} - \sqrt{5})