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
Rationalise the denominator of the following
`(sqrt2 + sqrt5)/3`
Rationalise the denominator of the following
`(3sqrt2)/sqrt5`
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`
`(sqrt2 - 1)/sqrt5`
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Simplify `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + sqrt12/(sqrt3 - sqrt2)`
Write the rationalisation factor of \[7 - 3\sqrt{5}\].
\[\sqrt[5]{6} \times \sqrt[5]{6}\] is equal to
Value of (256)0.16 × (256)0.09 is ______.
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
