Advertisements
Advertisements
प्रश्न
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
Advertisements
उत्तर
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
संबंधित प्रश्न
Represent `sqrt9.3` on the number line.
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Simplify the following:
`4sqrt12 xx 7sqrt6`
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
Simplify:
`[((625)^(-1/2))^((-1)/4)]^2`
