Advertisements
Advertisements
Question
Express the following with rational denominator:
`30/(5sqrt3 - 3sqrt5)`
Advertisements
Solution
We know that rationalization factor for `5sqrt3 - 3sqrt5` is `5sqrt3 + 3sqrt5`. We will multiply numerator and denominator of the given expression `30/(5sqrt3 - 3sqrt5)` by `5sqrt3 + 3sqrt5` to get
`30/(5sqrt3 - 3sqrt5) xx (5sqrt3 + 3sqrt5)/(5sqrt3 + 3sqrt5)`
= `(30 xx 5 xx sqrt3 + 30 xx 3 xx sqrt5)/(5(sqrt3)^2 - (3sqrt3)^2)`
`= (30 xx 5 xx sqrt3 + 30 xx 3 xx sqrt5)/(25 xx 3 - 9 xx 5)`
`= (30 xx 5 xx sqrt3 + 30 xx 3 xx sqrt5)/30`
`(150sqrt3 + 90sqrt5)/30`
`(150sqrt3)/30 + (90sqrt5)/30`
`= 5sqrt3 + 3sqrt5`
APPEARS IN
RELATED QUESTIONS
Rationalise the denominator of each of the following
`1/sqrt12`
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
In the following determine rational numbers a and b:
`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
The rationalisation factor of \[2 + \sqrt{3}\] is
Rationalise the denominator of the following:
`sqrt(40)/sqrt(3)`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
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.
