# TSI Math: Using Prime Factorization to Find Cubed Roots

What value when cubed is equal to -216x⁵?

Intermediate Algebra and Functions | Expressions, Equations, and Functions Involving Powers, Roots, and Radicals |

Mathematics and Statistics Assessment | Powers, Roots, and Radicals |

Product Type | TSI |

TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Intermediate Algebra and Functions |

TSI Mathematics | Intermediate Algebra and Functions |

Test Prep | TSI |

### Transcript

factors under the cube so it looks like this We've

got the cube root of negative to sixty next to

the fifth which is the same as the cube root

of negative one times cube root of to sixteen You

should recognize that to sixteen Number because it's a special

number We've got them the cube root of x to

the fifth as its multiple can there So that's what

It's gonna look like this Negative one to sixteen Fifty

Yeah Now it's Time to find each of these three

cube roots Slow and steady wins The race was going

to come one at a time Here we go Cube

root of negative one is negative one right Because negative

one two The third powers Negative one All right Once

that's done we'll turn our attention to the cube root

of to sixteen Start by finding the prime factors of

two sixteen there and so whole lot of threes And

you know this because you could add two plus one

plus six which gets you nine and that's evenly Divisible

by three So you know three is going to be

one of those factors right Well to do so we

keep dividing out Smalls primes is possible Is shown here

we got two Sixteen equals two times one Oh eh

with vehicles two times two times fifty for which equals

two times two times two two twenty seven which equals

all this stuff right here at the end of the

day It's two cubed times three cubed that's it Then

we separate the factors and that allows us to take

the cube roots here So cube root of to sixteen

is the cube root of two to the third times

three to the third which is same as the cube

root of two to the third which is just too

in the cube root of three to the third which

is just three So the freakin answer is six You

could have gotten there by knowing that six times six

is thirty six I'm six is two Sixteen that's What

we mean by it's one of those special numbers You'll

see that a lot of tests So you may I

just want to kind of note that in your brain

All right well specifically then we go to take the

cube root of x to the fifth by factoring out

an x cube there that's the same as x to

the three plus two which is same as x to

the third times x to the squared or to the

second power there orjust x squared So once again separate

the factors under the cube root symbol Here we've got

the cube root of exit third times x squared that

gives us the cube root of x cubed times the

cube root of x squared which equals x times the

cube root of x squared right there So we found

each of the three cube roots that we originally set

out to find So it's time to finish the problem

Put them all together and get your simplify on right

so cube root of negative one time's cube root of

to sixteen there times cube root of x fifth is

the same as native One time six times acts times

cube root of x squared which same as negative six

x times the cube root of x squared wow that

was ugly but were done And the answer is v 00:02:57.46 --> [endTime] and let's Just move on