Question

$\sqrt{15 + 10 \sqrt{2} } + \sqrt{15 - 10 \sqrt{2} }$
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Answer 1

Step-by-step explanation:

$\sqrt{5(3 + 2 \sqrt{2}) } + \sqrt{5(3 - 2 \sqrt{2}) } \\ = \sqrt{5} ( \sqrt{ {1}^{2} + { \sqrt{2} }^{2} + 2 \times 1 \times \sqrt{2} } + \sqrt{ {1}^{2} + { \sqrt{2} }^{2} - 2 \times 1 \times \sqrt{2} } \\ = \sqrt{5} ( \sqrt{ {( \sqrt{2} + 1) }^{2} } + \sqrt{ {( \sqrt{2} - 1) }^{2} } \\ = \sqrt{5} ( \sqrt{2} + 1 + \sqrt{2} - 1) \\ = \sqrt{5} \times 2 \sqrt{2} \\ = 2 \sqrt{10}$