How do you simplify a square root inside a square root?Please give me the explanation and an example, thanks!

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vixen999 | High School Teacher | (Level 2) Adjunct Educator

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Is there additional information available for your question?  I am not exactly sure what your question is asking.  There are a couple of examples that I could provide.  For example, you could have sqrt(sqrt(25)).  In this case, I would evaluate the inner square root of 25 which would give me 5.  Then, I would proceed to the outer square root and get an answer of sqrt(5).  Another example would be the sqrt(sqrt(x)).  We could write this as sqrt(x^1/2)  because we can write the square root as 1/2.  Then, we could write (x^1/2)^1/2.  Since this is a power raised to a power (or step ladder as I call it), we would multiple the exponents and end up with x^1/4 which could also be written as the 4th root of x.

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