Advertisements
Advertisements
प्रश्न
Rationalise the denominator of the following:
`sqrt(6)/(sqrt(2) + sqrt(3))`
उत्तर
Let `E = sqrt(6)/(sqrt(2) + sqrt(3))`
For rationalising the denominator, multiplying numerator and denominator by `sqrt(2) - sqrt(3)`,
`E = sqrt(6)/(sqrt(2) + sqrt(3)) xx (sqrt(2) - sqrt(3))/(sqrt(2) - sqrt(3))`
= `(sqrt(6)(sqrt(2) - sqrt(3)))/((sqrt(2))^2 - (sqrt(3))^2)` ...[Using identity, (a – b)(a + b) = a2 – b2]
= `(sqrt(6) (sqrt(2) - sqrt(3)))/(2 - 3)`
= `(sqrt(6)(sqrt(2) - sqrt(3)))/(-1)`
= `sqrt(6)(sqrt(3) - sqrt(2))`
= `sqrt(18) - sqrt(12)`
= `sqrt(9 xx 2) - sqrt(4 xx 3)`
= `3sqrt(2) - 2sqrt(3)`
APPEARS IN
संबंधित प्रश्न
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Simplify the following expressions:
`(sqrt8 - sqrt2)(sqrt8 + sqrt2)`
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt5 + 1)/sqrt2`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt10 + sqrt15)/sqrt2`
`
Simplify `(7 + 3sqrt5)/(3 + sqrt5) - (7 - 3sqrt5)/(3 - sqrt5)`
The rationalisation factor of \[2 + \sqrt{3}\] is
After rationalising the denominator of `7/(3sqrt(3) - 2sqrt(2))`, we get the denominator as ______.
Find the value of a and b in the following:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = a + 7/11 sqrt(5)b`
Find the value of `4/((216)^(-2/3)) + 1/((256)^(- 3/4)) + 2/((243)^(- 1/5))`
