Advertisements
Advertisements
Question
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
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
Rationalize the denominator.
`4/(7+ 4 sqrt3)`
Simplify by rationalising the denominator in the following.
`(1)/(5 + sqrt(2))`
Simplify the following
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
Simplify the following :
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`
In the following, find the values of a and b.
`(sqrt(3) - 1)/(sqrt(3) + 1) = "a" + "b"sqrt(3)`
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x3 + y3
If x = `sqrt3 - sqrt2`, find the value of:
(i) `x + 1/x`
(ii) `x^2 + 1/x^2`
(iii) `x^3 + 1/x^3`
(iv) `x^3 + 1/x^3 - 3(x^2 + 1/x^2) + x + 1/x`
Show that Negative of an irrational number is irrational.
Show that: `x^3 + 1/x^3 = 52`, if x = 2 + `sqrt3`
