Question

prove
$evaluate \: \frac{ \sqrt{5 } + \sqrt{3} }{ \sqrt{5 } - \sqrt{3 \: } } \: given \: that \: \sqrt{15 } = 3.87$

Answer 1

Hello,

The first step is to rationalise the given real number.
So,.on rationalization we get
$\frac{ \sqrt{5 } + \sqrt{3} }{ \sqrt{5 } - \sqrt{3 \: } } \\ = \frac{( \sqrt{5} + \sqrt{3} )( \sqrt{5} + \sqrt{3} )}{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3}) } \\ = \frac{ {( \sqrt{5} + \sqrt{3}) }^{2} }{ { \sqrt{5} }^{2} - { \sqrt{3} }^{2} } \\ = \frac{5 + 3 + 2 \sqrt{15} }{5 - 3 } \\ = \frac{8 + 2 \sqrt{15} }{2} \\ = \frac{2(4 + \sqrt{15} )}{2} = 4 + \sqrt{15}$
Also,

We have given that the value of root15 is equal to 3.87.

So ,
If we put the value in the simplified real number we can get the answer easily .
Putting values ....

$4 + \sqrt{15} = 4 + 3.87 = 7.87$
Hence,
The answer is 7.87

Hope this will be helping you ✌️