Factoring Cubed Roots

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When factoring cubed roots, first try to determine what number multiplied by itself three times will result in the given number. Find out how to break numbers up into a factor tree with help from a math teacher in this free video on basic math lessons.

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Video Transcript

So how does one factor cube roots? Hi, I'm Jimmy Chang. I've been teaching college mathematics for nine years. And we're here to introduce a couple of examples as to how to factor cubed roots. They seem intimidating at first but once you see what the strategy is you should be good to go. Now we're going to do one involving numbers and we're going to do another example involving variables. So here we go. Suppose you wanted to find out the cubed root of 64. Now basically what you want to ask yourself is what number multiplied by itself three times is going to give you 64? Well what you can do is you can break up 64 into a couple of ways. But first let's break up 64 into a factor tree. Now one such example and you can break up 64 as many ways as you want but just come up with two numbers that multiply to give you 64. Now 64 for example can be broken up by 16 times 4. Now 4 is pretty easy, you can break 4 up if you want to as well but you know 16 for sure needs to be broken up. Now two common numbers that multiply to give you 16 is 4 times 4. Now for right now let's think about leaving 64 as 4 times 4 times 4. And here's why. Because you know that 64 can be broken up as 4 times 4 times 4, there's a rule in algebra that lets us; that says you can break it up as those three numbers multiplied together. So it would be 4 times 4 times 4. Now with cubed roots since it is a cubed root that means for every three of the same number you can pull out one and there be nothing left. In other words because there's three 4's you can pull one of them out and the whole thing would be done. So in other words the cubed root of 64 would just be the number 4. It's a three for one trade when it comes to numbers. Now here's one involving variables. Suppose you wanted to find out the cube root of 6 to the 5th. For variables it's actually pretty straight forward as well. You actually treat it as a long division problem. You take the outside number which is a 3 and you divide it into the inside exponent which is the 5. Now what's 3 go into 5? Well 3 goes into 5, 1 time remainder 2. Now why is that important? The 1 is the exponent of X that gets to go out. In other words X to the first or X goes outside a radical. The remainder 2 tells you the exponent that stays in so that means X squared stays on the inside. In other words the cubed root of X to the 5th is X cubed root of X squared. So I'm Jimmy Chang and that's how you simplify cube roots.


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