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Simplify 3 times the principal root of 500x to the 3rd power. So what we're gonna do here is to try and

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break up the stuff we have under the radical sign into some things that are perfect squares, then we

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can separately take the square roots of those things and leave the left-overs inside of the radical

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sign. The other thing we have to remember is the principal square root, this radical sign here really

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means the positive square root of a number. So let's think about this a little bit. So let's see if we

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can break down the 500 x to the third into some perfect squares and some things that maybe aren't perfect

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squares, because 500 is not a perfect square, x to the third is not a perfect square, right from the

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get-go. So, when in doubt, we can just start to prime factorize this and maybe we'll discover some perfect

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squares. So 500 is divisible by 5 and its 5 times 100, and you probably already recognize that 100 is

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a perfect square. It is 10 times 10. But if you didn't know that, you could just keep factoring. You

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could say a 100 is 2 times 50 , 50 is 2 times 25 and 25 is 5 times 5. So, you'd see the perfect squares

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here , coz you would see, you would see two 2s, you have a 2 times two and you have a 5 times a 5. So

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you could really just say that a 100 is 10 times 10 or you could say its 2 squared times 5 squared.

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Either of those things would allow you to break this down. And then x to the third is, just clearly,

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the same thing as x to the third, right over here, is clearly the same thing as x squared times x, which

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allows us to break it down into perfect squares and something that is not a perfect square. So let's

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just rewrite these numbers under the principal root sign. So, this is going to be equal to 3 times ,

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I'll save some space here, 3 times the 500, I could rewrite it as a 100 times 5 and a 100 I could write

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as 10 squared. So this right here, I could write as 10 squared, I don't have to do all of this business

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down here, but this will help you recognize that this is a perfect square. Its 4 times 25 , and those

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are perfect squares. So a 100 is 10 squared, I'm gonna write this as 10 squared squared, 10 times squared