Question

$\sqrt{ - \sqrt 3 + \sqrt{84 + 18 \sqrt{3} } }$

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Answer 1

Step-by-step explanation:

$\sqrt{ - \sqrt{3} + \sqrt{84 + 18 \sqrt{3} } } \\ = \sqrt{ - \sqrt{3} + \sqrt{81 + 3 + 18 \sqrt{3} } } \\ = \sqrt{ - \sqrt{3} + \sqrt{ {9}^{2} + { (\sqrt{3}) }^{2} + 2 \times 9 \times \sqrt{3} } } \\ = \sqrt{ - \sqrt{3} + \sqrt{(9 + \sqrt{3} ) {}^{2} } } \\ = \sqrt{ - \sqrt{3} + 9 + \sqrt{3} } \\ = \sqrt{9 } \\ = 3$