SarkariPYQ

SSC CGL 2025 PYQ — Question 57

SSC CGL - 19 Sep 2025 - Shift 2 • Quantitative Aptitude • Q57

Back to paper

Evaluate: (11+7)2−(11−7)2\left(\sqrt{11}+\sqrt7 \right)^2-\left(\sqrt{11}-\sqrt7 \right)^2

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 4774\sqrt{77}.

a2 - b2 = (a - b)(a + b)

(11+7)2−(11−7)2\left(\sqrt{11}+\sqrt7 \right)^2-\left(\sqrt{11}-\sqrt7 \right)^2

=[(11+7)−(11−7)]×[(11+7)+(11−7)]=[(\sqrt{11} + \sqrt{7}) - (\sqrt{11} - \sqrt{7})] \times [(\sqrt{11} + \sqrt{7}) + (\sqrt{11} - \sqrt{7})]  

=(27)×(211)=(2\sqrt{7}) \times (2\sqrt{11})

=477=4\sqrt{77}