Question

rationalise the denominator 1/√3+√5​

Answer 1

Step-by-step explanation:

REFER TO THE ATTACHMENT

Answer 2

$\sf{ \frac{1}{ \sqrt{3} + \sqrt{5}}}$

The denominator can be rationalised by Multiplying with the opposite sign of the denominator , with the same number as numerator as well as the denominator.

So , following the above step we get :

$\sf{ \frac{1}{ \sqrt{3} + \sqrt{5} }} \times {\frac {\sqrt{3} - \sqrt{5}}{\sqrt{3} - \sqrt{5}}}$

If we carefully observe the denominator ; it is in the form of (a + b) (a - b)

We know that it's expansion gives $\sf{ {a}^{2} - {b}^{2}}$

So , we do the same.

$\sf{ 1 \times \sqrt{3} - \sqrt{5} = \sqrt{3} - \sqrt{5}}$-----> this will be our numerator

$\sf{ \frac{ \sqrt{3} - \sqrt{5}}{ {\sqrt{3}}^{2} - \sqrt{5}^{2}}}$

This gives us :

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

Thus we get :

$\sf{\frac {\sqrt{3}-\sqrt{5}}{-2}}$

When we interchange the places of the digits in numerator we get :

$\huge\boxed{\sf {\frac{\sqrt{5} - \sqrt{2}}{2}}}$

Hence we have rationalised the denominator..