Advertisements
Advertisements
Question
Simplify:
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
Advertisements
Solution
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
= `[ sqrt2]/[ sqrt6 - 2] - [ sqrt3 ]/[ sqrt6 + sqrt2 ] `
`= [ sqrt2( sqrt6 + sqrt2) - sqrt3( sqrt6 - sqrt2 )]/[ (sqrt6 - sqrt2)- (sqrt 6 + sqrt2)]`
= `[ sqrt12 + 2 - sqrt18 + sqrt6 ]/[ (sqrt6)^2 - (sqrt2)^2 ]`
= `[ 2sqrt3 + 2 - 3sqrt2 + sqrt6 ]/(6 - 2)`
= `[ 2sqrt3 + 2 - 3sqrt2 + sqrt6 ]/4`
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`1/(sqrt 7 + sqrt 2)`
Rationalise the denominators of : `[ 2 - √3 ]/[ 2 + √3 ]`
Simplify by rationalising the denominator in the following.
`(sqrt(15) + 3)/(sqrt(15) - 3)`
If `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) = "p" + "q"sqrt(30)`, find the values of p and q.
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
In the following, find the values of a and b:
`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`
If x = `(7 + 4sqrt(3))`, find the values of :
`(x + (1)/x)^2`
If x = `(4 - sqrt(15))`, find the values of
`(1)/x`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of
x2 - y2 + xy
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
