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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
Rationalise the denominator of the following
`(sqrt3 + 1)/sqrt2`
Express each one of the following with rational denominator:
`(b^2)/(sqrt(a^2 + b^2) + a)`
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
Write the rationalisation factor of \[7 - 3\sqrt{5}\].
Write the rationalisation factor of \[\sqrt{5} - 2\].
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.
`4/sqrt(3)`
Simplify:
`(256)^(-(4^((-3)/2))`
