Advertisements
Advertisements
Question
Rationalise the denominator and simplify `(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6))`
Advertisements
Solution
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)) = ((2sqrt(6) - sqrt(5))(3sqrt(5) + 2sqrt(6)))/((3sqrt(5) - 2sqrt(6))(3sqrt(5) + 2sqrt(6))`
= `(6sqrt(6 xx 5) + 4 xx sqrt(6 xx 6) - sqrt(5) xx 3sqrt(5) - 2 xx sqrt(5 xx 6))/((3sqrt(5))^2 - (2sqrt(6))^2`
= `(6sqrt(30) + 4 xx 6 - 3 xx 5 - 2sqrt(30))/(45 - 24)`
= `(sqrt(30)(6 - 2) + 24 - 15)/21`
= `(9 + 4sqrt(30))/21`
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`6/(9sqrt 3)`
Rationalize the denominator.
`11 / sqrt 3`
Write the simplest form of rationalising factor for the given surd.
`4 sqrt 11`
Write the lowest rationalising factor of : √18 - √50
Write the lowest rationalising factor of : 3√2 + 2√3
Find the values of 'a' and 'b' in each of the following :
`[2 + sqrt3]/[ 2 - sqrt3 ] = a + bsqrt3`
If x = `2sqrt3 + 2sqrt2`, find: `1/x`
If x = 2√3 + 2√2, find: `(x + 1/x)`
Rationalise the denominator `sqrt(75)/sqrt(18)`
Rationalise the denominator and simplify `sqrt(5)/(sqrt(6) + 2) - sqrt(5)/(sqrt(6) - 2)`
