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प्रश्न
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
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उत्तर
We know that rationalization factor for `6 + 4sqrt2` is `6 - 4sqrt2`. We will multiply numerator and denominator of the given expression `(6 - 4sqrt2)/(6 + 4sqrt2)` by `6 - 4sqrt2` to get
`(6 - 4sqrt2)/(6 + 4sqrt2) xx (6 - 4sqrt2)/(6 - 4sqrt2) = (6^2 + (4sqrt2)^2 - 2 xx 6 4 sqrt2)/((6)^2 - (4sqrt2)^2)`
` (36 + 16 xx 2 - 48sqrt2)/(36 - 16 xx 2)`
`= (36 + 32 - 48sqrt2)/(36 - 32)`
`= (68 - 48sqrt2)/4`
`= 17 - 12sqrt2`
Hence the given expression is simplified with rational denominator to `17 - 12sqrt2`
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संबंधित प्रश्न
Simplify the following expressions:
`(sqrt5 - 2)(sqrt3 - sqrt5)`
Rationalise the denominator of each of the following
`1/sqrt12`
Rationalise the denominator of the following
`(sqrt2 + sqrt5)/3`
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
If x = \[\sqrt{5} + 2\],then \[x - \frac{1}{x}\] equals
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
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.
`1/(sqrt(3) + sqrt(2))`
Simplify:
`(1/27)^((-2)/3)`
Simplify:
`[((625)^(-1/2))^((-1)/4)]^2`
