Advertisements
Advertisements
Question
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Advertisements
Solution
Let `E = (3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
For rationalising the denominator, multiplying numerator and denominator by `sqrt(5) + sqrt(3)`,
`E = (3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) xx (sqrt(5) + sqrt(3))/(sqrt(5) + sqrt(3))`
= `(3sqrt(5)(sqrt(5) + sqrt(3)) + sqrt(3)(sqrt(5) + sqrt(3)))/((sqrt(5))^2 - (sqrt(3))^2` ...[Using identity, (a + b)(a – b) = a2 – b2]
= `(15 + 3sqrt(15) + sqrt(15) + 3)/(5 - 3)`
= `(18 + 4sqrt(15))/2`
= `9 + 2sqrt(15)`
APPEARS IN
RELATED QUESTIONS
Classify the following numbers as rational or irrational:
`2-sqrt5`
Simplify the following expressions:
`(4 + sqrt7)(3 + 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`
`
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
Express each one of the following with rational denominator:
`(b^2)/(sqrt(a^2 + b^2) + a)`
In the following determine rational numbers a and b:
`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`
Simplify `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + sqrt12/(sqrt3 - sqrt2)`
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Simplify the following:
`3sqrt(3) + 2sqrt(27) + 7/sqrt(3)`
If `x = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))` and `y = (sqrt(3) - sqrt(2))/(sqrt(3) + sqrt(2))`, then find the value of x2 + y2.
