Question

Simplify it by rationalising the denominator
√7-√5/√7+√5

Answer 1

Hey friend

Here is your answer

$= \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} } \\ \\ = \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} } \times \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} - \sqrt{5} } \\ \\ = \frac{ {( \sqrt{7} - \sqrt{5} )}^{2} }{( \sqrt{7} + \sqrt{5}) ( \sqrt{7} - \sqrt{5)} } \\ \\ using \: following \: identities \\ \\ 1) {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ 2)(a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{ ({ \sqrt{7} )}^{2} + {( \sqrt{5} )}^{2} - 2 \times \sqrt{7} \times \sqrt{5} }{ {( \sqrt{7} )}^{2} - {( \sqrt{5} )}^{2} } \\ \\ = \frac{7 + 5 - 2 \sqrt{35} }{7 - 5} \\ \\ = \frac{12 - 2 \sqrt{35} }{2} \\ \\ = \frac{2(6 - \sqrt{35)} }{2} \\ \\ = 6 - \sqrt{35}$

Hope this helps you ☺

Answer 2

Hey friend !!!!

•°• Refer to the attached file •°•

Hope it satisfies you ☆▪☆

Thanks ^_^

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