Advertisements
Advertisements
Question
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
Advertisements
Solution
We know that rationalization factor for `sqrt5 - sqrt3` and `sqrt5 + sqrt3` are `sqrt5 + sqrt3` and `sqrt5 - sqrt3` respectively.
We will multiply numerator and denominator of the given expression `(sqrt5 + sqrt3)/(sqrt5 - sqrt3)` and `(sqrt5 - sqrt3)/(sqrt5 + sqrt3)` by `sqrt5 + sqrt3` and `sqrt5 + sqrt3` respectively, to get
`(sqrt5 + sqrt3)/(sqrt5 - sqrt3) xx (sqrt5 + sqrt3)/(sqrt5 + sqrt3) + (sqrt5 - sqrt3)/(sqrt5 + sqrt3) xx (sqrt5 - sqrt3)/(sqrt5 - sqrt3) = ((sqrt5)^2 + (sqrt3)^2 + 2 xx sqrt5 xx sqrt3)/((sqrt5)^2- (sqrt3)^2)`
`(5 + 3 + 2sqrt15)/(5- 3) + (5 + 3 - 2sqrt15)/(5 - 3)`
`= (5 + 3 + 2sqrt15 + 5 + 3 - 2sqrt15)/2`
= 16/2
= 8
Hence the given expression is simplified to 8
APPEARS IN
RELATED QUESTIONS
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`
Express the following with rational denominator:
`30/(5sqrt3 - 3sqrt5)`
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
\[\sqrt[5]{6} \times \sqrt[5]{6}\] is equal to
Value of `root(4)((81)^-2)` is ______.
Simplify the following:
`sqrt(45) - 3sqrt(20) + 4sqrt(5)`
Rationalise the denominator of the following:
`(3 + sqrt(2))/(4sqrt(2))`
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))`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
