Advertisements
Advertisements
Question
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
Advertisements
Solution
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
= `(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)) xx (5sqrt(3) - sqrt(15))/(5sqrt(3) - sqrt(15)`
= `((5sqrt(3) - sqrt(15))^2)/((5sqrt(3))^2 - (sqrt(15))^2`
= `(75 + 15 - 10sqrt(45))/(75 - 15)`
= `(90 - 10sqrt(45))/(60)`
= `(9 - 1sqrt(45))/(6)`
= `(9 - 3sqrt(5))/(6)`
= `(3 - sqrt(5))/(2)`
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`4/(7+ 4 sqrt3)`
Rationalize the denominator.
`2/(3 sqrt 7)`
Rationalise the denominators of : `3/sqrt5`
Simplify by rationalising the denominator in the following.
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
If `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) = "p" + "q"sqrt(30)`, find the values of p and q.
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
If x = `(7 + 4sqrt(3))`, find the values of :
`(x + (1)/x)^2`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
Using the following figure, show that BD = `sqrtx`.
