Exams › SSC CGL (Prelims) › General

Evaluate: \((\sqrt{13}+\sqrt{5})^2-(\sqrt{13}-\sqrt{5})^2\).

1. 4 \(\sqrt{65}\)
2. 2 \(\sqrt{65}\)
3. 8 \(\sqrt{65}\)
4. 36

Correct answer: 4 \(\sqrt{65}\)

Solution

Using the identity \((a+b)^2-(a-b)^2=4ab\), the expression becomes \(4\sqrt{13}\sqrt{5}\). Since \(\sqrt{13}\sqrt{5}=\sqrt{65}\), the result is \(4\sqrt{65}\).

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