Advertisements
Advertisements
Question
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))`
Advertisements
Solution
Let `E = 1/(sqrt(3) + sqrt(2))`
For rationalising the denominator multiplying numerator and denominator by `sqrt(3) - sqrt(2)`, we get
= `1/(sqrt(3) + sqrt(2)) xx (sqrt(3) - sqrt(2))/(sqrt(3) - sqrt(2))`
= `(sqrt(3) - sqrt(2))/((sqrt(3))^2 - (sqrt(2)^2)`
= `(sqrt(3) - sqrt(2))/(3 - 2)`
= `sqrt(3) - sqrt(2)` ...`["Put" sqrt(3) = 1.732 "and" sqrt(2) = 1.414]`
= 1.732 – 1.414
= 0.318
APPEARS IN
RELATED QUESTIONS
Simplify the following expressions:
`(4 + sqrt7)(3 + sqrt2)`
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`
`3/sqrt10`
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:
`30/(5sqrt3 - 3sqrt5)`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(1 + sqrt2)/(3 - 2sqrt2)`
Simplify the following expression:
`(sqrt5-sqrt2)(sqrt5+sqrt2)`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
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.
`6/sqrt(6)`
Find the value of `4/((216)^(-2/3)) + 1/((256)^(- 3/4)) + 2/((243)^(- 1/5))`
