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प्रश्न
Express the following with rational denominator:
`1/(3 + sqrt2)`
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उत्तर
We know that rationalization factor for `3 + sqrt2` is `3 - sqrt2`. We will multiply numerator and denominator of the given expression `1/(3 + sqrt2)` by `3 - sqrt2` to get
`1/(3 + sqrt2) xx (3 - sqrt2)/(3 - sqrt2) = (3 - sqrt2)/(3^2 - (sqrt2)^2)`
`= (3 - sqrt2)/(9 - 2)`
`= (3 - sqrt2)/7`
Hence the given expression is simplified with rational denominator to `(3 - sqrt2)/7`
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संबंधित प्रश्न
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)`
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
If x = \[\sqrt{5} + 2\],then \[x - \frac{1}{x}\] equals
Classify the following number as rational or irrational:
`1/sqrt2`
Simplify the following expression:
`(sqrt5+sqrt2)^2`
Simplify the following:
`3/sqrt(8) + 1/sqrt(2)`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
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.
`6/sqrt(6)`
