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प्रश्न
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
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उत्तर
We know that rationalization factor for `3 - 2sqrt2` is `3 + 2sqrt2`. We will multiply numerator and denominator of the given expression `(1 + sqrt2)/(3 - 2sqrt2)` by `3 + 2sqrt2`
`(1 + sqrt2)/(3 - 2sqrt2) xx (3 + 2sqrt2)/(3 + 2sqrt2) = (3 + 2sqrt2 + 3sqrt2 + 2 xx (sqrt2)^2)/((3)^2 - (2sqrt2)^2)`
` = (3 + 5sqrt2 + 4)/(9 - 4 xx 2)`
`= (7 + 5sqrt2)/(9 - 8)`
`= (7 + 5sqrt2)/1`
`= 7 + 5sqrt2`
Hence the given expression is simplified to `7 + 5sqrt2`
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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`
`(sqrt10 + sqrt15)/sqrt2`
`
In the following determine rational numbers a and b:
`(4 + sqrt2)/(2 + sqrt2) = n - sqrtb`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
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:
`1/sqrt2`
The number obtained on rationalising the denominator of `1/(sqrt(7) - 2)` is ______.
After rationalising the denominator of `7/(3sqrt(3) - 2sqrt(2))`, we get the denominator as ______.
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
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`
Simplify:
`(1/27)^((-2)/3)`
