Question

30/5√3-3√5

note:5√3 and -3√5 are both in the denominator

Answer 1

нєℓℓσ мαтє!

нєяє ιѕ υσυя ѕσℓυтισи

30 / ( 5√3 - 3√5 )

Rationalize

30 / ( 5√3 - 3√5 ) × ( 5√3 + 3√5 )/( 5√3 + 3√5 )
30 ( 5√3 + 3√5 )/ ( 25*3 - 9*5 )
30 ( 5√3 + 3√5 )/ ( 75 - 45 )
30 ( 5√3 + 3√5 ) / 30

Here, 30 cancelled out

αиѕωєя : 5√3 + 3√5

нσρє ιт нєℓρѕ

Answer 2

$\frac{30}{5 \sqrt{3} - 3 \sqrt{5} } \\ \\ \\ by \: rationalization \\ \\ \\ \frac{30(5 \sqrt{3} + 3 \sqrt{5}) }{(5 \sqrt{3} - 3 \sqrt{5})(5 \sqrt{3} + 3 \sqrt{5} )} \\ \\ \\ \\ \frac{30(5 \sqrt{3} + 3 \sqrt{5}) }{ {(5 \sqrt{3} )}^{2} - {(3 \sqrt{5} )}^{2} } \\ \\ \\ \\ \frac{30(5 \sqrt{ 3} + 3 \sqrt{5}) }{75 - 45} \\ \\ \\ \frac{30(5 \sqrt{3} + 3 \sqrt{5}) }{30} \\ \\ \\ 5 \sqrt{3} + 3 \sqrt{5}$