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प्रश्न
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
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
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`(2sqrt5 + 3sqrt2)^2`
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`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt10 + sqrt15)/sqrt2`
`
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`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
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Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
