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If \[\Sqrt{5^N} = 125\] Then `5nsqrt64`= - Mathematics

MCQ

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.

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Q 32 | Page 32
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