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Question
If \[\sqrt{5^n} = 125\] then `5nsqrt64`=
Options
25
\[\frac{1}{125}\]
625
\[\frac{1}{5}\]
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Solution
We have to find `5nsqrt64` provided \[\sqrt{5^n} = 125\]
So,
`sqrt 5^n = 125`
`5^(nxx 1/2)= 5^3`
`n/2 = 3`
`n=3xx2`
` n =6`
Substitute ` n =6` in `5nsqrt64` to get
` `5nsqrt64 = 5^(2^(6x1/6)`
=` 5^(2^(6x1/6)`
`= 5xx5`
`=25`
Hence the value of `5nsqrt64` is 25.
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