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
Classify the following numbers as rational or irrational:
`2-sqrt5`
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
\[\sqrt{10} \times \sqrt{15}\] is equal to
Classify the following number as rational or irrational:
2π
After rationalising the denominator of `7/(3sqrt(3) - 2sqrt(2))`, we get the denominator as ______.
Value of `root(4)((81)^-2)` is ______.
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
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))`
If `a = (3 + sqrt(5))/2`, then find the value of `a^2 + 1/a^2`.
