Advertisements
Advertisements
Question
Rationalise the denominator and simplify `(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6))`
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`
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 :
x2
If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find m2
If x = 2√3 + 2√2 , find : `( x + 1/x)^2`
If x = 5 - 2√6, find `x^2 + 1/x^2`
Rationalise the denominator and simplify `sqrt(5)/(sqrt(6) + 2) - sqrt(5)/(sqrt(6) - 2)`
Find the value of a and b if `(sqrt(7) - 2)/(sqrt(7) + 2) = "a"sqrt(7) + "b"`
