Question

what is the smallest number by which √5 - √3 be multiplied to make it a rational no.?
also find the no. so obtained.

Answer 1

We know, by Rationalisation, 

(√5 - √3)(√5 + √3) = (√5)² - (√3)² = 5 - 3 = 2 which is rational

Answer 2

To make (sqrt a - sqrt b) rational we

have to multiply with it's conjugate i.e

(sqrt a + sqrt b)

Here conjugate of ( sqrt 5 - sqrt 3 ) is

( sqrt 5 + sqrt 3)

Verification:

(sqrt 5 - sqrt 3 ) ( sqrt 5 + sqrt 3)

= ( sqrt 5)^2 - (sqrt 3)^2

= 5 - 3

= 2 (rational number)

I hope this will useful to u