Question

Rationalise the denomination of 5/√3-√5​

Answer 1

Given to Rationalize :-

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

Solution :-

First what is Rationalization. Rationalization means In denominator we have to remove surds For removing surds We have to multiply with its Rationalizing factor

Rationalizing factor means just we have to change the sign .

So,

Rationalizing factor for ,

$\sqrt{3 } - \sqrt{5} \: \: is \: \: \sqrt{3} + \sqrt{5}$

So, multiply and divide with that

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

$\dfrac{5( \sqrt{3} + \sqrt{5} )}{( \sqrt{3} - \sqrt{5})( \sqrt{3} + \sqrt{5} ) }$

Denominator is in form of (a + b) (a -b) = a²-b²

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

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

$\dfrac{5 \sqrt{3} + 5 \sqrt{5} }{ - 2}$

$\dfrac{ - (5 \sqrt{3} + 5 \sqrt{5}) }{2}$

$\dfrac{ - 5 \sqrt{3} - 5 \sqrt{5} }{2}$

Hence in denominator radicals or surds removed .So, denomiantor rationalized

So,

$\dfrac{5}{ \sqrt{3} - \sqrt{5} }$ = $\dfrac{ - 5 \sqrt{3} - 5 \sqrt{5} }{2}$