Question

rationalise......please solve this question......please..

Answer 1

i hope it to be correct.....

Answer 2

To rationalize, here we should multiply the denominator by 5√3 +3√5 as well as numerator.

So
$\frac{5 \sqrt{3 } + 3 \sqrt{5} }{5 \sqrt{3} - 3 \sqrt{5} } \times \frac{5 \sqrt{3} + 3 \sqrt{5} }{5 \sqrt{3} + 3\sqrt{5} }$
I'm the denominator we can use the identity
(a + b)(a -b ) = a² - b²
and in numerator we can use (a +b)² = a² + b² + 2ab

=>
$\frac{(5 \sqrt{3} + 3 \sqrt{5}) {}^{2} }{(5 \sqrt{3} ) {}^{2} - (3 \sqrt{} 5) {}^{2} } \\ = \frac{25 \times 3 + 9 \times 5 + 2 \times 5 \sqrt{3 } \times 3 \sqrt{5} }{25 \times 3 - 9 \times 5} \\ = \frac{75 + 45 + 30 \sqrt{15} }{75 - 45} \\ = \frac{120 + 30 \sqrt{} 15}{30} \\ = \frac{30 (4 + 1 \sqrt{15} )}{30}$
now cancelling 30 with 30 we get

$4 + 1 \sqrt{15}$
=
$4 + \sqrt{15}$
Hope it helps dear friend ☺️✌️