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प्रश्न
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
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उत्तर
We know that rationalization factor for `2sqrt5 - sqrt3` is `2sqrt5 + sqrt3`. We will multiply numerator and denominator of the given expression `1/(2sqrt5 - sqrt3)` by `2sqrt5 + sqrt3` to get
`1/(2sqrt5 - sqrt3) xx (2sqrt5 + sqrt3)/(2sqrt5 + sqrt3) = (2sqrt5 + sqrt3)/((2sqrt5)^2 - (sqrt3)^2)`
`= (2sqrt5 + sqrt3)/(4 xx 5 - 3)`
`= (2sqrt5 + sqrt3)/(20 - 3)`
`= (2sqrt5 + sqrt3)/17`
`= 5sqrt3 + 3sqrt5`
Hence the given expression is simplified with rational denominator to `(2sqrt5 + sqrt3)/17`
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संबंधित प्रश्न
Rationalise the denominator of the following
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`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
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Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
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Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
The rationalisation factor of \[\sqrt{3}\] is
Simplify the following:
`(2sqrt(3))/3 - sqrt(3)/6`
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
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