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प्रश्न
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
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उत्तर
We know that rationalization factor for `3sqrt5 - 2sqrt6` is `3sqrt5 + 2sqrt6` . We will multiply numerator and denominator of the given expression `(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)` by `3sqrt5 + 2sqrt6` to get
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6) xx (3sqrt5 + 2sqrt6)/(2sqrt + 2 sqrt6) = (2xx 3 xx sqrt6 + sqrt5 + (2sqrt6)^2 - 3 xx (sqrt5)^2 - 2 xx sqrt5 xx sqrt6)/((3sqrt5)^2 - (2sqrt6)^2)`
`= (6sqrt(6 xx 5) + 4 xx 6 - 3 xx (sqrt5)^2 - 2 xx sqrt5 xx sqrt6)/(9 xx 5 - 4 xx 6)`
` = (6sqrt30 + 24 - 15 - 2sqrt30)/(45 - 24)`
`= (9 + 4sqrt30)/21`
Hence the given expression is simplified to `(9 + 4sqrt30)/21`
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संबंधित प्रश्न
Rationalise the denominator of each of the following
`3/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`
`(sqrt10 + sqrt15)/sqrt2`
`
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
Simplify
`1/(2 + sqrt3) + 2/(sqrt5 - sqrt3) + 1/(2 - sqrt5)`
If\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y\sqrt{3},\] find the values of x and y.
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
\[\sqrt{10} \times \sqrt{15}\] is equal to
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.
`4/sqrt(3)`
If `sqrt(2) = 1.414, sqrt(3) = 1.732`, then find the value of `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`.
If `a = (3 + sqrt(5))/2`, then find the value of `a^2 + 1/a^2`.
