Advertisements
Advertisements
प्रश्न
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
Advertisements
उत्तर
We know that rationalization factor for `sqrt3 + sqrt2` is "sqrt3 - sqrt2". We will multiply numerator and denominator of the given expression `(sqrt3 - sqrt2)/(sqrt3 + sqrt2)` by `sqrt3 - sqrt2` to get
`(sqrt3 - sqrt2)/(sqrt3 + sqrt2) xx (sqrt3 - sqrt2)/(sqrt3 - sqrt2) = ((sqrt3)^2 + (sqrt2)^2 - 2 sqrt3 xx sqrt2)/((sqrt3)^2 - (sqrt2)^2)`
`= (3 + 2 - 2sqrt6)/(3 - 2)`
`= (5 - 2sqrt6)/1`
`= 5 - 2sqrt6`
Hence the given expression is simplified to `5 - 2sqrt6`
APPEARS IN
संबंधित प्रश्न
Simplify of the following:
`root(3)4 xx root(3)16`
Simplify the following expression:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
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:
`16/(sqrt41 - 5)`
Simplify `(7 + 3sqrt5)/(3 + sqrt5) - (7 - 3sqrt5)/(3 - sqrt5)`
Classify the following number as rational or irrational:
`1/sqrt2`
Simplify the following expression:
`(sqrt5-sqrt2)(sqrt5+sqrt2)`
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
Simplify:
`64^(-1/3)[64^(1/3) - 64^(2/3)]`
If `x = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))` and `y = (sqrt(3) - sqrt(2))/(sqrt(3) + sqrt(2))`, then find the value of x2 + y2.
