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प्रश्न
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
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उत्तर
We know that rationalization factor for `sqrt3 + sqrt2` is "sqrt3 - sqrt2". We will multiply numerator and denominator of the given expression `(sqrt3 - sqrt2)/(sqrt3 + sqrt2)` by `sqrt3 - sqrt2` to get
`(sqrt3 - sqrt2)/(sqrt3 + sqrt2) xx (sqrt3 - sqrt2)/(sqrt3 - sqrt2) = ((sqrt3)^2 + (sqrt2)^2 - 2 sqrt3 xx sqrt2)/((sqrt3)^2 - (sqrt2)^2)`
`= (3 + 2 - 2sqrt6)/(3 - 2)`
`= (5 - 2sqrt6)/1`
`= 5 - 2sqrt6`
Hence the given expression is simplified to `5 - 2sqrt6`
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संबंधित प्रश्न
Rationalise the denominator of each of the following
`1/sqrt12`
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Classify the following number as rational or irrational:
2π
Simplify the following expression:
`(sqrt5-sqrt2)(sqrt5+sqrt2)`
Rationalise the denominator of the following:
`1/(sqrt7-sqrt6)`
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`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
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`3/sqrt(8) + 1/sqrt(2)`
Rationalise the denominator of the following:
`2/(3sqrt(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(2)/(2 + sqrt(2)`
