SOLUTION: What is the square root of (5mn)^5

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Question 367254: What is the square root of (5mn)^5
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28%285mn%29%5E5%29
To simplify any square root you look for perfect square factors. So we will factor the radicand (the expression inside the radical) into as many perfect square factors as possible:
sqrt%285%5E5m%5E5n%5E5%29
sqrt%285%5E2%2A5%5E2%2A5%2Am%5E2%2Am%5E2%2Am%2An%5E2%2An%5E2%2An%29
Using the Commutative property we can rearrange the factors. I like to put all the perfect square factors in front:
sqrt%285%5E2%2A5%5E2%2Am%5E2%2Am%5E2%2An%5E2%2An%5E2%2A5%2Am%2An%29
Next we can use the property of radicals, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29+%2A+root%28a%2C+q%29 to separate all the perfect square factors into separate square roots:

Now we can simplify the square roots of the perfect squares:
5%2A5%2Am%2Am%2An%2An%2Asqrt%285%2Am%2An%29
which simplifies to:
25m%5E2%2An%5E2%2Asqrt%285mn%29