Question

If \[\sqrt{5^n} = 125\] then  `5nsqrt64`=

Options

• 25

• \[\frac{1}{125}\]

• 625 

• \[\frac{1}{5}\]

Answer 1

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.