Exams › SSC CGL (Prelims) › General

Simplify: \(\sqrt{7+4\sqrt{3}} + \sqrt{7-4\sqrt{3}}\).

1. 2
2. 2 \(\sqrt{3}\)
3. 4
4. 4 \(\sqrt{3}\)

Correct answer: 4

Solution

We can write \(7+4\sqrt{3} = (\sqrt{3}+2)^2\) and \(7-4\sqrt{3} = (2-\sqrt{3})^2\). Therefore, the expression becomes \((\sqrt{3}+2) + (2-\sqrt{3}) = 4\).

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