The value of the fourth root of $56 - 24 \sqrt{5}$

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$(\sqrt{5} + 2)$

$(\sqrt{5} - 2)$

$(\sqrt{5} - 1)$

$(\sqrt{5} + 1)$

answer is A.

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Detailed Solution

$\begin{array}{l} \sqrt[4]{56 - 24 \sqrt{5}} \\ = \sqrt{56 - \sqrt{36 \times 20}} \\ = \sqrt{\sqrt{36} - \sqrt{20}} \\ = \sqrt{6 - 2 \sqrt{5}} \\ = (\sqrt{5} - 1) \end{array}$

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