Advertisements
Advertisements
Question
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
Solution
Let `E = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
For rationalising the denominator, multiplying numerator and denominator by `sqrt(3) + sqrt(2)`,
`E = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2)) xx (sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2))`
= `(sqrt(3) + sqrt(2))^2/((sqrt(3))^2 - (sqrt(2))^2` ...[Using identity, (a – b)(a + b) = a2 – b2]
= `((sqrt(3))^2 + (sqrt(2))^2 + 2sqrt(3)sqrt(2))/(3 - 2)` ...[Using identity, (a + b)2 = a2 + b2 + 2ab]
= `3 + 2 + 2sqrt(6)`
= `5 + 2sqrt(6)`
APPEARS IN
RELATED QUESTIONS
Simplify the following expressions:
`(5 + sqrt7)(5 - sqrt7)`
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Simplify the following expression:
`(sqrt5-sqrt2)(sqrt5+sqrt2)`
`root(4)root(3)(2^2)` equals to ______.
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
Simplify the following:
`3/sqrt(8) + 1/sqrt(2)`
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`sqrt(2)/(2 + sqrt(2)`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
