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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
Classify the following numbers as rational or irrational:
`2-sqrt5`
Rationalise the denominator of the following:
`1/sqrt7`
Simplify the following expressions:
`(sqrt5 - 2)(sqrt3 - sqrt5)`
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
Rationalise the denominator of the following:
`3/(2sqrt5)`
Rationalise the denominator of each of the following
`1/sqrt12`
Express each one of the following with rational denominator:
`(b^2)/(sqrt(a^2 + b^2) + a)`
Simplify the following:
`(sqrt(3) - sqrt(2))^2`
Simplify the following:
`3/sqrt(8) + 1/sqrt(2)`
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))`
