Advertisements
Advertisements
प्रश्न
Simplify `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + sqrt12/(sqrt3 - sqrt2)`
Advertisements
उत्तर
We know that rationalization factor for `3sqrt2 + 2sqrt3` and `sqrt3 - sqrt2` are `3sqrt2 - 2sqrt3` and `sqrt3 + sqrt2`respectively. We will multiply numerator and denominator of the given expression `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3)` and `sqrt12/(sqrt3 - sqrt2)` by `3sqrt2 - 2sqrt3` and `sqrt3 + sqrt2` respectively to get
`(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) xx (3sqrt2 - 2sqrt3)/(3sqrt2 - 2sqrt3) + sqrt12/(sqrt3 - sqrt2) xx (sqrt3 + sqrt2)/(sqrt3 + sqrt2) = ((3sqrt2)^2 + (2sqrt3)^2 - 2 xx 3sqrt2 xx 2sqrt3)/((3sqrt2)^2 - (2sqrt3)^2) + (sqrt36 + sqrt24)/((sqrt3)^2 - (sqrt2)^2)`
`= (18 + 12 - 12sqrt6)/(18 - 12) + (6 + sqrt24)/(3 - 2)`
`= (30 - 12sqrt6 + 36 + 12sqrt6)/6`
`= 66/6`
= 11
Hence the given expression is simplified to 11
APPEARS IN
संबंधित प्रश्न
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`
`(sqrt5 + 1)/sqrt2`
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
If \[x = 2 + \sqrt{3}\] , find the value of \[x + \frac{1}{x}\].
The rationalisation factor of \[2 + \sqrt{3}\] is
Simplify the following expression:
`(3+sqrt3)(3-sqrt3)`
The number obtained on rationalising the denominator of `1/(sqrt(7) - 2)` is ______.
After rationalising the denominator of `7/(3sqrt(3) - 2sqrt(2))`, we get the denominator as ______.
Simplify the following:
`sqrt(45) - 3sqrt(20) + 4sqrt(5)`
Simplify:
`(1/27)^((-2)/3)`
Simplify:
`(8^(1/3) xx 16^(1/3))/(32^(-1/3))`
