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प्रश्न
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
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उत्तर
We know that rationalization factor for `sqrt6 - sqrt5` is `sqrt6 + sqrt5`. We will multiply numerator and denominator of the given expression `1/(sqrt6 -sqrt5)` by `sqrt6 + sqrt5` to get
`1/(sqrt6 - sqrt5) xx (sqrt6 + sqrt5)/(sqrt6 + sqrt5) = (sqrt6 + sqrt6)/((sqrt6)^2 - (sqrt5)^2`
`= (sqrt6 + sqrt5)/(6 - 5)`
`= (sqrt6 + sqrt5)/(6 - 5)`
`= (sqrt6 + sqrt5)/1`
`= sqrt6 + sqrt5`
Hence the given expression is simplified with rational denominator to `sqrt6 + sqrt5`.
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संबंधित प्रश्न
Simplify the following expressions:
`(5 + sqrt7)(5 - sqrt7)`
Rationalise the denominator of each of the following
`3/sqrt5`
Rationalise the denominator of the following
`sqrt2/sqrt5`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
The rationalisation factor of \[\sqrt{3}\] is
Simplify the following expression:
`(sqrt5+sqrt2)^2`
Simplify the following:
`(sqrt(3) - sqrt(2))^2`
Simplify the following:
`(2sqrt(3))/3 - sqrt(3)/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))`
Simplify:
`(1/27)^((-2)/3)`
