Advertisements
Advertisements
Question
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
Advertisements
Solution
We know that rationalization factor for `2sqrt5 - sqrt3` is `2sqrt5 + sqrt3`. We will multiply numerator and denominator of the given expression `1/(2sqrt5 - sqrt3)` by `2sqrt5 + sqrt3` to get
`1/(2sqrt5 - sqrt3) xx (2sqrt5 + sqrt3)/(2sqrt5 + sqrt3) = (2sqrt5 + sqrt3)/((2sqrt5)^2 - (sqrt3)^2)`
`= (2sqrt5 + sqrt3)/(4 xx 5 - 3)`
`= (2sqrt5 + sqrt3)/(20 - 3)`
`= (2sqrt5 + sqrt3)/17`
`= 5sqrt3 + 3sqrt5`
Hence the given expression is simplified with rational denominator to `(2sqrt5 + sqrt3)/17`
APPEARS IN
RELATED QUESTIONS
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = `c/d`. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Simplify the following expressions:
`(3 + sqrt3)(3 - sqrt3)`
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`
`
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
In the following determine rational numbers a and b:
`(4 + sqrt2)/(2 + sqrt2) = n - sqrtb`
Rationalise the denominator of the following:
`1/(sqrt7-sqrt6)`
Rationalise the denominator of the following:
`sqrt(6)/(sqrt(2) + sqrt(3))`
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
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.
`1/(sqrt(3) + sqrt(2))`
If `sqrt(2) = 1.414, sqrt(3) = 1.732`, then find the value of `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`.
