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SSC CHSL 2025 PYQ — Question 67

SSC CHSL - 29 Nov 2025 - Shift 3 • Quantitative Aptitude • Q67

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Simlify the Equation:

326+3−436+2+63+2 \frac{3\sqrt{2}}{\sqrt{6}+\sqrt{3}} - \frac{4\sqrt{3}}{\sqrt{6}+\sqrt{2}} + \frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}

Show answer & explanation

Correct answer: C

Explanation

Given:

(3√2)/(√6 + √3) − (4√3)/(√6 + √2) + (√6)/(√3 + √2)

By the formula:

(a + b)(a − b) = a² − b²

(3√2)/(√6 + √3) × (√6 − √3)/(√6 − √3)

= 3√2(√6 − √3)/(6 − 3)

= √2(√6 − √3)

= 2√3 − √6

(4√3)/(√6 + √2) × (√6 − √2)/(√6 − √2)

= 4√3(√6 − √2)/(6 − 2)

= √3(√6 − √2)

= 3√2 − √6

(√6)/(√3 + √2) × (√3 − √2)/(√3 − √2)

= √6(√3 − √2)/(3 − 2)

= √18 − √12

= 3√2 − 2√3

(2√3 − √6) − (3√2 − √6) + (3√2 − 2√3)

= 2√3 − √6 − 3√2 + √6 + 3√2 − 2√3

= 0