Advertisements
Advertisements
Question
Simplify the following :
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`
Advertisements
Solution
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`
Rationalizing the denominator of each term, we have
= `(4sqrt(3)(2 + sqrt(2)))/((2 - sqrt(2))(2 + sqrt(2))) - (30(4sqrt(3) + 3sqrt(2)))/((4sqrt(3) - 3sqrt(2))(4sqrt(3) + 3sqrt(2))) - (3sqrt(2)(3 - 2sqrt(3)))/((3 + 2sqrt(3))(3 - 2sqrt(3))`
= `(8sqrt(3) + 4sqrt(6))/(4 - 2) - (120sqrt(3) + 90sqrt(2))/(48 - 18) - (9sqrt(2) - 6sqrt(6))/(9 - 12)`
= `(8sqrt(3) + 4sqrt(6))/(2) - (120sqrt(3) + 90sqrt(2))/(30) - (9sqrt(2) - 6sqrt(6))/(-3)`
= `(8sqrt(3) + 4sqrt(6))/(2) - (120sqrt(3) + 90sqrt(2))/(30) - (9sqrt(2) - 6sqrt(6))/(3)`
= `4sqrt(3) + 2sqrt(6) - 4sqrt(3) - 3sqrt(2) + 3sqrt(2) - 2sqrt(6)`
= 0
APPEARS IN
RELATED QUESTIONS
Rationalise the denominators of : `(2sqrt3)/sqrt5`
Rationalise the denominators of:
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
Simplify:
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
Simplify by rationalising the denominator in the following.
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
Simplify by rationalising the denominator in the following.
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
If x = `(4 - sqrt(15))`, find the values of
`x^3 + (1)/x^3`
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
