Advertisements
Advertisements
Question
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
Advertisements
Solution
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
Rationalizing the denominator of each term, we have
= `(6(2sqrt(3) + sqrt(6)))/((2sqrt(3) - sqrt(6))(2sqrt(3) + sqrt(6))) + (sqrt(6)(sqrt(3) - sqrt(2)))/((sqrt(3) + sqrt(2))(sqrt(3) - sqrt(2))) - (4sqrt(3)(sqrt(6) + sqrt(2)))/((sqrt(6) - sqrt(2))(sqrt(6) + sqrt(2))`
= `(12sqrt(3) + 6sqrt(6))/(12 - 6) + (sqrt(18) - sqrt(12))/(3 - 2) - (4sqrt(18) + 4sqrt(6))/(6 - 2)`
= `(12sqrt(3) + 6sqrt(6))/(6) + (sqrt(18) - sqrt(12))/(1) - (4sqrt(18) + 4sqrt(6))/(4)`
= `2sqrt(3) + sqrt(6) + sqrt(18) - sqrt(12) - sqrt(18) - sqrt(6)`
= `2sqrt(3) - sqrt(12)`
= `2sqrt(3) - 2sqrt(3)`
= 0
APPEARS IN
RELATED QUESTIONS
Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`
Rationalise the denominator of `1/[ √3 - √2 + 1]`
Simplify : `sqrt18/[ 5sqrt18 + 3sqrt72 - 2sqrt162]`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
In the following, find the value of a and b:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
If x = `(7 + 4sqrt(3))`, find the value of
`x^2 + (1)/x^2`
If x = `(4 - sqrt(15))`, find the values of
`(1)/x`
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
