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
Simplify by rationalising the denominator in the following.
`(sqrt(15) + 3)/(sqrt(15) - 3)`
Simplify by rationalising the denominator in the following.
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
Simplify by rationalising the denominator in the following.
`(7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)`
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
Simplify the following
`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`
Simplify the following :
`sqrt(6)/(sqrt(2) + sqrt(3)) + (3sqrt(2))/(sqrt(6) + sqrt(3)) - (4sqrt(3))/(sqrt(6) + sqrt(2)`
If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x2 - y2) = `144sqrt(5)`.
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
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)`
Draw a line segment of length `sqrt8` cm.
