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 expression:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Simplify the following expression:
`(sqrt5+sqrt2)^2`
`root(4)root(3)(2^2)` equals to ______.
Simplify the following:
`(sqrt(3) - sqrt(2))^2`
Rationalise the denominator of the following:
`sqrt(40)/sqrt(3)`
Rationalise the denominator of the following:
`(3 + sqrt(2))/(4sqrt(2))`
Simplify:
`[((625)^(-1/2))^((-1)/4)]^2`
