Advertisements
Advertisements
Question
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
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
Represent `sqrt9.3` on the number line.
Simplify the following expressions:
`(sqrt5 - 2)(sqrt3 - sqrt5)`
Simplify the following expressions:
`(5 + sqrt7)(5 - sqrt7)`
Rationalise the denominator of the following
`(3sqrt2)/sqrt5`
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
Classify the following number as rational or irrational:
`1/sqrt2`
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
Simplify the following:
`3sqrt(3) + 2sqrt(27) + 7/sqrt(3)`
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
