Question

Salmonpanna2022 please solve that question.
Only this question I am asking from Salmon.​

Answer 1

Step-by-step explanation:

पश्न:

$\sqrt{4 - \sqrt{7} } + \sqrt{8 + 3 \sqrt{7} }$

उत्तर:

$\sqrt{2} ( \sqrt{7} + 1)$

$\sqrt{4 - \sqrt{7} } - \sqrt{8 + 3\sqrt{7} } \\ = > \sqrt{ \frac{(4 - \sqrt{7}) \times 2 }{2} } + \sqrt{ \frac{(8 + 3 \sqrt{7}) \times 2 }{2} } \\ = > \sqrt{ \frac{8 - 2 \sqrt{7} }{2} } + \sqrt{ \frac{16 + 6 \sqrt{7} }{2} } \\ = > \sqrt{ \frac{( \sqrt{7})^{2} + 1 - 2 \sqrt{2} }{2} } \\ \sqrt{ \frac{( {3})^{2} +( \sqrt{7} ) ^{2} + 2 \times 3 \times \sqrt{7} }{2} } \\ = > \sqrt{ \frac{( { \sqrt{7 } - 1 )}^{2} }{2} } + \sqrt{ \frac{3 + ( { \sqrt{7} )}^{2} }{2} } \\ = > \frac{ \sqrt{7} - 1}{ \sqrt{2} } + \frac{3 + \sqrt{7} }{ \sqrt{2} } \\ = > \frac{ \sqrt{7} - 1 + 3 + \sqrt{7} }{ \sqrt{2} } = \frac{2 \sqrt{7} + 2 }{ \sqrt{2} } \\ = > \frac{ \sqrt{2} ( \sqrt{2} \times \sqrt{7} + \sqrt{2} ) }{ \sqrt{2} } = \sqrt{2} ( \sqrt{7} + 1) \: \: ans.$

${ }^{i \: hope \: its \: help \: you.}$