Home
Class 10
MATHS
Remove the irrationality in the denomina...

Remove the irrationality in the denominator `1/(1+sqrt(2)+sqrt(3))`

Text Solution

Verified by Experts

`1/(1+sqrt2+sqrt3) = 1/(sqrt3+sqrt2+1)**(sqrt3-(sqrt2+1))/(sqrt3-(sqrt2+1))`
`=(sqrt3-(sqrt2+1))/(sqrt3^2- (sqrt2+1)^2)`
`=(sqrt3-sqrt2-1)/(3-2-1-2sqrt2 )`
`=(sqrt3-sqrt2-1)/(-2sqrt2 )`
`=(sqrt3-sqrt2-1)/(-2sqrt2 )**(-sqrt2)/(-sqrt2)`
`=(-sqrt6+2+sqrt2)/4`
`=(2+sqrt2-sqrt6)/4`, which is the required solution.
Promotional Banner

Similar Questions

Explore conceptually related problems

Remove the irrationality in the denominator a. sqrt((sqrt(2)-1)/(sqrt(2)+1)) b. 1/(1+sqrt(2)+sqrt(3))

Remove the irrationality in the denominator a.sqrt((sqrt(2)-1)/(sqrt(2)+1)) b.(1)/(1+sqrt(2)+sqrt(3))

Rationalize the denominator 1/(sqrt(5)-sqrt(3))

Rationalise the denominator of 1/(sqrt(2))

rationalising the denominator: (1)/(3sqrt2-2sqrt3)

Rationalise the denominator of 1/(3+sqrt(2))

Rationalise the denominator of 1/(3+sqrt(2))

Rationalize the denominator of (1)/(sqrt(2))

Rationalise the denominator of (1)/(sqrt(2))

Rationalize the denominator: 1/(3sqrt(5)+2sqrt(2))