Question

Simplify
$( \sqrt{3} - \sqrt{5} )( \sqrt{3} + \sqrt{5} ) \div 7 - \sqrt[2]{5}$

Answer 1

Hey friend,
Here is the answer:
$\frac{( \sqrt{3} - \sqrt{5} )( \sqrt{3} + \sqrt{5}) }{ 7 - \sqrt[2]{5} } \\ \\ using \: identities \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{ {( \sqrt{3} )}^{2} - {( \sqrt{5}) }^{2} }{7 - \sqrt{5} } \times \frac{7 + \sqrt{5} }{7 + \sqrt{5} } \\ \\ = \frac{3 - 5}{7 - \sqrt{5} } \times \frac{7 + \sqrt{5} }{7 + \sqrt{5} } \\ \\ again \: using \: same \: identity \\ \\ = \frac{ - 2 \times 7 - 2 \times \sqrt{5} }{ {(7)}^{2} - {( \sqrt{5} )}^{2} } \\ \\ = \frac{ - 14 - 2 \sqrt{5} }{49 - 5} \\ \\ = \frac{ - 14 - 2 \sqrt{5} }{ 44} \\ \\ = \frac{ - 7 - \sqrt{5} }{22}$

Hope this helps!!!

@Mahak24

Thanks...
☺☺

Answer 2

$Given : ( \sqrt{3} - \sqrt{5} ) \frac{( \sqrt{3} + \sqrt{5} ) }{7} - \sqrt{5}$

$\frac{( \sqrt{3} + \sqrt{5} )( \sqrt{3} - \sqrt{5} ) }{7} - \sqrt{5}$

$\frac{-2}{7} - \sqrt{5}$

$\frac{-2 - 7 \sqrt{5} }{7}$


Hope this helps!