Question

rationalize:

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

Answer 1

RATIONALISATION:-

It is a mathematical method in which an irrational denominator of a number can become rational without changing its orignal value.

$example \\ \frac{7}{ \sqrt{2} }$

For converting denominator to rational number we have to multiply root 2 in denominator but it may change the value of orignal number. Therefore, we have to multiply the number with root2 by root 2 so its value remain as multiplying a number with 1 remains the same number.

$\frac{7}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{7 \sqrt{2} }{2}$

Now If denominator has two terms like in your question then we have to just multiply the number by interchanging the middle one in order to apply the identity :-

( a + b )( a - b) = a^2 - b^2

YOUR ANSWER :-

$\frac{5}{ \sqrt{3}+ \sqrt{5}} \\ \\ = \frac{5}{ \sqrt{3} + \sqrt{5} } \times \frac{ \sqrt{3} - \sqrt{5} }{ \sqrt{3} - \sqrt{5} } \\ \\ = \frac{5( \sqrt{3} - \sqrt{5} )}{3 - 5} \\ \\ = \frac{5( \sqrt{3} - \sqrt{5}) }{ - 2} \\ \\ = \frac{ - 5( \sqrt{3} - \sqrt{5} )}{2} \: (ans)$