SOLUTION: Simplify 5 to the 5 halves power

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Question 90032: Simplify

5 to the 5 halves power
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given expression

root%282%2C5%5E5%29 Rewrite using the identity x%5E%28a%2Fb%29=root%28b%2Cx%5Ea%29

So this root is a square root

sqrt%285%5E5%29

sqrt%283125%29 Evaluate 5%5E5 to get 3125


Now lets simplify the square root:

The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.
So let's list the factors of 3125
Factors:
1, 5, 25, 125, 625, 3125


Notice how 625 is the largest perfect square, so lets factor 3125 into 625*5


sqrt%28625%2A5%29 Factor 3125 into 625*5

sqrt%28625%29%2Asqrt%285%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

25%2Asqrt%285%29 Take the square root of the perfect square 625 to get 25

So the expression sqrt%283125%29 simplifies to 25%2Asqrt%285%29

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Answer:
So the expression simplifies to 25%2Asqrt%285%29 which is about 55.9017 in decimal form