$\sqrt{8 + \sqrt{44}} - \sqrt{8 - \sqrt{44}}=$ ?

Correct answer marked below

-2\sqrt{4 - \sqrt{5}}

2\sqrt{4 - \sqrt{5}}

Correct

2\sqrt{4 + \sqrt{5}}

2\sqrt{11}

4\sqrt{11}

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Explanation

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Official Explanation

Official

Let the output of the expression = x

\sqrt{8 + \sqrt{44}} - \sqrt{8 - \sqrt{44}} = x

Squaring both sides:

8 + \sqrt{44} + 8 - \sqrt{44} - 2(\sqrt{8 + \sqrt{44}} \cdot \sqrt{8 - \sqrt{44}}) = x^2

16 - 2(\sqrt{(8 + \sqrt{44})(8 - \sqrt{44})}) = x^2

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What this question tests

Your handling of square and higher roots, including simplifying radicals.

Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.