Question

please answer this question fast
$\sqrt{2 + \sqrt{5} - \sqrt{6 - 3 \sqrt{5} + \sqrt{14 - 6 \sqrt{5} } } }$

Answer 1

Hi...☺

Here is your answer...✌

$\sqrt{2 + \sqrt{5} - \sqrt{6 - 3 \sqrt{5} + \sqrt{14 - 6 \sqrt{5} } } } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: .....(1) \\ \\ first \: we \: calculate \\ \\ \sqrt{14 - 6 \sqrt{5} } \\ \\ = \sqrt{9 + 5 - 6 \sqrt{5} } \\ \\ = \sqrt{ {3}^{2} + {( \sqrt{5})}^{2} - 2 \times 3 \times \sqrt{5} } \\ \\ = \sqrt{{(3 - \sqrt{5})}^{2} } \\ \\ = 3 - \sqrt{5} \\ \\ on \: putting \: this \: value \: in \: (1)\: \\ we \: have \\ \\ \sqrt{2 + \sqrt{5} - \sqrt{6 - 3 \sqrt{5} + 3 - \sqrt{5} } } \\ \\ = \sqrt{2 + \sqrt{5} - \sqrt{9 - 4 \sqrt{5} } } \\ \\ = \sqrt{2 + \sqrt{5} - \sqrt{ 5 + 4- 4 \sqrt{5} } } \\ \\ = \sqrt{2 + \sqrt{5} - \sqrt{ { (\sqrt{5})}^{2} + {2}^{2} - 2 \sqrt{5} \times 2 } } \\ \\ = \sqrt{2 + \sqrt{5} - \sqrt{{( \sqrt{5} - 2) }^{2} } } \\ \\ = \sqrt{2 + \sqrt{5} - ( \sqrt{5} - 2) } \\ \\ = \sqrt{2 + \sqrt{5} - \sqrt{5} + 2} \\ \\ = \sqrt{2 + 2} = \sqrt{4} \\ \\ = 2$

Answer 2

your answer is 2

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