Question

rationalize : 5 / root 3 - root 5​

Answer 1

Answer :

$\tt{ \dfrac{5}{\sqrt{3} - \sqrt{5}}}$

For rationalising the denominator ; first we will check the sign in the given rational number .

In the case of the given number its (-) so ; we will multiply it's positive form with both the numerator and the denominator.

$\tt{ \dfrac{5}{\sqrt{3} - \sqrt{5}} \times \dfrac{\sqrt{3}+\sqrt{5}}{\sqrt{3} + \sqrt{5}}}$

If we carefully observe the denominators ; they are in the $\tt{ (a+b) (a-b) }$ identity where (a) in this condition is $\tt{ \sqrt{3}}$ and (b) is $\tt{ \sqrt{5}}$.

The expansion of $\tt{ (a+b) (a-b) }$ identity is $\tt{ {a}^{2} - {b}^{2}}$.

So we will put the same identity for solving the problem.

If we do so ; it gives us :

$\tt{ \dfrac{5 \times \sqrt{3} + \sqrt{5}}{{(\sqrt{3})}^{2} + {(\sqrt{5})}^{2}}}$

When further simplified gives us :

$\tt{ \dfrac{5\sqrt{3+5}}{3 - 5}}$

$\large{\boxed{\tt{ \implies \dfrac{5\sqrt{3+5}}{-2}}}}$

Answer 2

This is the answer you should follow to be top in maths