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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:
`(3 + sqrt3)(5 - sqrt2)`
Simplify the following expressions:
`(sqrt3 + sqrt7)^2`
Rationalise the denominator of each of the following
`3/sqrt5`
Rationalise the denominator of each of the following
`1/sqrt12`
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
Rationales the denominator and simplify:
`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
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.
`(sqrt(10) - sqrt(5))/2`
