Question

please solve this question​

Answer 1

Answer:

$2 \sqrt{6}$

Step-by-step explanation:

$\sqrt{7 + 2 \sqrt{6} } = \sqrt{ {( \sqrt{6}) }^{2} + {1}^{2} + 2( \sqrt{6})(1) } \\ \\ = \sqrt{ {( \sqrt{6} + 1) }^{2} } \\ \\ = \sqrt{6} + 1 \\ \\ \\ \sqrt{7 - 2 \sqrt{6} } = \sqrt{ {( \sqrt{6}) }^{2} + {1}^{2} - 2( \sqrt{6} )(1) } \\ \\ = \sqrt{ {( \sqrt{6} - 1) }^{2} } \\ \\ = \sqrt{6} - 1 \\ \\ then \: \: \: \: \: \: \: \sqrt{7 + 2 \sqrt{6} } + \sqrt{7 - 2 \sqrt{6} } = \sqrt{6 } + 1 + \sqrt{6} - 1 \\ \\ = 2 \sqrt{6}$