Working with radicals has a few restrictions associated with it that you're going to want to keep in mind. Learn about restrictions with radicals with help from an expert in mathematics in this free video clip.

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Working with radicals has a few restrictions associated with it that you're going to want to keep in mind. Learn about restrictions with radicals with help from an expert in mathematics in this free video clip.

Part of the Video Series: Radical Numbers

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Hey there it's Dr. K with Infinite Magic Productions and in today's tutorial we're going to learn about radicals. Mostly we're going to learn about the rules and restrictions of using radicals. So the rules for radicals are, basic rules are, if you have a radical, we'll say a radical of a with an index of n and if the index of n is odd, it's an odd number so you have a cubic root or the root to the 5th power, then a, the radical of a is going to be equal to a. On the other hand, if the index is even, so it's a square root, the 4th root, the 6th root, then the radical with an even index is going to be the absolute power of a. We'll make these stars. So likewise the next rule is going to be, if the radical of a to the n power of n and a is greater or equal to zero then this property of radical of a to the n power, the radical of it is going to be equal to a. This is a simple way of looking at radicals and what it's going to be equal to. Basically what this expression is saying that if a is to the n power and you're taking the radical with an index of n power and a is greater than zero then this expression is basically equal to a. Now the restrictions are if you have something that looks like this. The radical of a b so it's an equation with a radical to the n power. So this basically is not going to equal the same as the radical of a to the n power plus the radical of b to the n power. What this comes from is that if you take the radical of a times the radical of b to the n power this can equal to a. The radical of a to the n power times the radical of b to the n power. So basically it's the same as looking at this equation where a*b is the same as giving each of those variables it's own radical. Likewise if you have something that looks like this, a to the n power minus b to the n power and it's under a radical of n then also it does not equal a-b. So basically if you have multiplication or division within the radical, such as we have here, then you can simplify it and take those two radicals apart. So you have a with its own radical and b with its own radical. With division it would be the same. But if you have addition or subtraction underneath a radical then it does not simplify into a simple expression such as a-b. Because this would not allow that multiplication and division underneath the radical would simplify into you being able to take those radicals apart. But addition and subtraction would not. So remember kids, the rules, that addition and subtraction underneath a radical don't simplify. So there you have it. Those are some rules and restrictions for doing math with radicals. Thanks for watching and come back for more. I'm Dr. K .