Question

rationalise the denominator of 5/root 3-root5

Answer 1

=5/√3-√5×√3+√5/√3+√5
=5√3+5√5/-2

Answer 2

First of all,

What is 'Rationalisation'?

Rationalisation : It is a process to change the irrational number into a rational number by multipling with some suitable irrational numbers.

The factor which multipling to the given irrational number to change as irrational is called a "Rationalisation factor".


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Q. Rationalise the denominator of 5/(√3 - √5)

Solution :

5/(√3 - √5) × (√3 + √5)/(√3 + √5)

= [ 5×(√3 + √5) ] / [ (√3)² - (√5)² ]

= 5 × [ √3 + √5 / ( 3 - 5 ) ]

= 5 × [ √3 + √5 / ( -2 ) ]

= -5/2 ( √3 + √5 )