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प्रश्न
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
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उत्तर
We know that rationalization factor for `2sqrt5 - 3` is `2sqrt5 + 3`. We will multiply numerator and denominator of the given expression `(3sqrt2 + 1)/(2sqrt5 - 3)` by `2sqrt5 + 3` to get
`(3sqrt2 + 1)/(2sqrt5 - 3) xx (2sqrt5 + 3)/(2sqrt5 + 3) = (3sqrt2 xx 2sqrt5 + 3 xx 3sqrt2 + 2sqrt5 + 3)/((2sqrt5)^2 - (3)^2)`
`= (3 xx 2 xx sqrt2 xx sqrt5 + 3 xx 3sqrt2 + 2sqrt5 + 3)/(4 xx 5 - 9)`
`= (6sqrt(2 xx 5) + 9 sqrt2 + 2sqrt5 + 3)/(4 xx 5 - 9)`
`= (6sqrt10 + 9sqrt2 + 2sqrt5 + 3)/11`
Hence the given expression is simplified with rational denominator to `(6sqrt10 + 9sqrt2 + 2sqrt5 + 3)/11`
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संबंधित प्रश्न
Simplify the following expression:
`(3+sqrt3)(2+sqrt2)`
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`(2sqrt5 + 3sqrt2)^2`
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
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`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) = a - bsqrt77`
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`4sqrt12 xx 7sqrt6`
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`16/(sqrt(41) - 5)`
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
Find the value of a and b in the following:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = a + 7/11 sqrt(5)b`
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`
