Question

rationalise the denominator :√2. / √2+√3-√5​

Answer 1

Answer:

by rationalising

answer is

(2√6+√15+6)/12

Answer 2

Answer:

(√6+3+√15)/6

Step-by-step explanation:

To do: Rationalise the denominator   :√2. / √2+√3-√5​

Concept : Rationalisation of denominator of a number. Rationalising the denominator means the process of moving a root, for instance, a cube root or a square root from the bottom of a fraction (denominator) to the top of the fraction (numerator).

Process:

To rationalise the denominator we have to first multiply both the numerator and the denominator of the fraction by (√2+√3+√5).

This gives us :-

[√2×(√2+√3+√5)]÷(√2+√3-√5)×(√2+√3+√5)

= [2+√6+√10]÷[(√2+√3)²-5)]

= [2+√6+√10]÷[5+2√6-5]

= [2+√6+√10]÷2√6

(multiplying numerator and denominator  again by √6)

={[2+√6+√10]×√6}÷2√6×√6

=(2√6+6+2√15)/12

=(√6+3+√15)/6

(This is the required answer)

#SPJ2