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प्रश्न
Simplify:
`[((625)^(-1/2))^((-1)/4)]^2`
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उत्तर
`[((625)^(-1/2))^((-1)/4)]^2 = [((25^2)^(-1/2))^(-1/4)]^2` ...[∵ (am)n = amn]
= `(25^-1)^(-1/4 xx 2)`
= `[(5^2)^-1]^(-1/4 xx 2)`
= `5^(-2 xx -1/4 xx 2)`
= 51
= 5
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संबंधित प्रश्न
Rationalise the denominator of each of the following
`1/sqrt12`
Rationalise the denominator of the following
`(3sqrt2)/sqrt5`
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`
Express the following with rational denominator:
`1/(3 + sqrt2)`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
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)`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
