Question

rationalize the denominator 3/√5-√3

Answer 1

Step-by-step explanation:

$\large \tt \purple{\frac{3}{ \sqrt{5} - \sqrt{3} } } \\ \\ \large \tt = \frac{3}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } \\ \\ \large \tt= \frac{3( \sqrt{5} + \sqrt{3} )}{ {( \sqrt{5} })^{2} - {( \sqrt{3} })^{2} } \\ \\ \large \tt= \frac{3 \sqrt{5} + 3 \sqrt{3} }{5 - 3} \\ \\ \large \tt \pink{= \frac{3 \sqrt{5} + 3 \sqrt{3} }{2} }$

Answer 2

Step-by-step explanation:

$\frac{3}{ \sqrt{5} - \sqrt{3} }$

$= > \frac{3}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5 + \sqrt{3} } }$

$= > \frac{3 \sqrt{5} + 3 \sqrt{3} }{( \sqrt{5}) {}^{2} - ( \sqrt{3}) {}^{2} }$

$= > \frac{3 \sqrt{5} + 3 \sqrt{3} }{5 - 3}$

$= > \frac{3 \sqrt{5} + 3 \sqrt{3} }{2}$