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)`
Write the simplest form of rationalising factor for the given surd.
`sqrt 32`
Write the simplest form of rationalising factor for the given surd.
`sqrt 50`
Write the lowest rationalising factor of 5√2.
Find the values of 'a' and 'b' in each of the following:
`( sqrt7 - 2 )/( sqrt7 + 2 ) = asqrt7 + b`
Find the values of 'a' and 'b' in each of the following:
`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`
Find the values of 'a' and 'b' in each of the following:
`[5 + 3sqrt2]/[ 5 - 3sqrt2] = a + bsqrt2`
If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : y2
Show that :
`1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2] = 5`
If x = `sqrt(5) + 2`, then find the value of `x^2 + 1/x^2`
