Question

Root 5 - root 3 ÷ root 5 + root 3 = ?

Answer 1

Hi there !!

Multiply denominator and numerator by its conjugate.

Identity used :-

(a-b)² = a²+b²-2ab

$\frac{ \sqrt{5 } - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ \\ \frac{( \sqrt{5} - \sqrt{3}) {}^{2} }{5 - 3} \\ \\ \frac{5 + 3 - 2\sqrt{15} }{2 } \\ \\ \frac{8 - 2\sqrt{15} }{2}$

Thankyou :)

Answer 2

Answer:-

Also,Refer the attachment

(a-b)² = a²+b²-2ab

$\begin{lgathered}\frac{ \sqrt{5 } - \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \\ \\ \frac{( \sqrt{5} - \sqrt{3}) {}^{2} }{5 - 3} \\ \\ \frac{5 + 3 - 2\sqrt{15} }{2 } \\ \\ \frac{8 - 2\sqrt{15} }{2}\end{lgathered}$