How to Factor Cubed Roots
To factor cubed roots, break down each term into common factors, find the perfect cube of each, and solve the problem until the remaining terms cannot be broken down further. Factor out cubed roots with information from a standardized test prep instructor in this free video on education.
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Let's take a look at how to break apart a cubic root. So first of all, here's what a cubic root is. So that's a cube root. This reads the cube root of eight. Now if this had just been the root bar, the square root bar and the eight, it would say the square root of eight. But the little tiny three here by this part indicates we want the cube root. If it was a four, we'd want the fourth root. Okay, so first of all this is a perfect cube. The answer to the cube root of eight is two. So that one's just done. But let's say it wasn't done. Let's just say we just, we had to break it apart. So if we had 16 X to the fourth and we want to break this apart to the cube root. Okay, so the way we would do that is we'd say we've got to break these apart. We've got to factor them, break them down into their factors. And the only factors we're interested in, we're not interested in normal factors here, we're only interested in perfect cube factors. The perfect cubes are: one cubed is one, that doesn't help much, two cubed is eight, three cubed is 27, and what I mean by that is three times three times three, 27. That's three cubed. Four cubed is 64, that's four times four times four. One more, five cubed is 125, and you can make a whole list. That's the only numbers we're interested in. So when we look at this number here, we're going to see, do any of these go into it? And you start at the top. The higher the better because then you'll have less reducing later, or less work later. So does 125 go in? No. Does 64 go in? No. Does 27 go in? No. Does 8 go in? Yes. So we break 16 apart as 8x2. Now X to the fourth. We're going to break that down to be X cubed and X because X cubed times X, which is really X to the first, is X to the fourth. We broke it down so there's a cube. That one's even easier to see, in a sense, than the numbers because you don't need your list. You just want to take out a cubed and then have whatever is left over there. Now here's why we did it. Because the cube root of eight is two. That comes out. The cube root of eight, as I showed you here is two. It's like the cube root of eight is a synonym for two. It just is two. When you cross it out, it comes out of the root sign as a two. The cube root of X cubed is X. You know, it's like saying what cubed is X cubed? X. And what we're left with inside the cube root, now you have to remember to write with three there, what we're left with inside the cube root sign is this guy and this guy. So when we break apart the cube root of 16 X to the fourth, we get a two and an X outside the cube root and inside the cube root we still have a two and an X.