Question

√7 - √5 / √2 + √ 3 , solve

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{2} + \sqrt{3} } \\ \\ on \: rationalizing \: we \: get \\ \\ \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ \frac{ \sqrt{7} \times \sqrt{2} - \sqrt{7} \times \sqrt{3} - \sqrt{5} \times \sqrt{2} + \sqrt{5} \times \sqrt{3} }{ {( \sqrt{2} )}^{2} - {( \sqrt{3} )}^{2} } \\ \\ = \frac{ \sqrt{14} - \sqrt{21} - \sqrt{10} + \sqrt{15} }{2 - 3} \\ \\ = - ( \sqrt{14} - \sqrt{21} - \sqrt{10} + \sqrt{15} ) \\ \\ = - \sqrt{14} + \sqrt{21} + \sqrt{10} - \sqrt{15} \\ \\ = \sqrt{10} - \sqrt{14} - \sqrt{15} + \sqrt{21}$

Hope this helps!!!

@Mahak24

Thanks...
☺☺

Answer 2

Hi ,

( √7 - √5 ) / ( √2 + √3 )

= [(√7-√5)(√3-√2)]/[(√3+√2)(√3-√2)]

= ( √21-√14-√15+√10 )/[(√3)²-(√2)²]

= √21 - √14 - √15 + √10

I hope this helps you.

: )