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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
Classify the following numbers as rational or irrational:
`2-sqrt5`
Simplify the following expression:
`(3+sqrt3)(2+sqrt2)`
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`
`(2 + sqrt3)/3`
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(1 + sqrt2)/(3 - 2sqrt2)`
Classify the following number as rational or irrational:
2π
Simplify the following:
`(sqrt(3) - sqrt(2))^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))`
Simplify:
`(1/27)^((-2)/3)`
