Exams › SSC CGL (Prelims) › General

Which of the following equals 20?

1. (\sqrt{8} + \sqrt{2})^2 - 4\sqrt{16}
2. (\sqrt{9} + \sqrt{11})^2
3. (\sqrt{6} + \sqrt{4})^2 + 2\sqrt{24}
4. (\sqrt{13} + \sqrt{7})^2 - 2\sqrt{91}

Correct answer: (\sqrt{13} + \sqrt{7})^2 - 2\sqrt{91}

Solution

For \((\sqrt{13} + \sqrt{7})^2 - 2\sqrt{91}\), expanding gives 13 + 7 + 2\sqrt{91} - 2\sqrt{91} = 20. The radical terms cancel exactly, leaving 20.

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