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TSI Math: Using Prime Factorization to Find Cubed Roots 14 Views


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Description:

What value when cubed is equal to -216x⁵?


Transcript

00:03

Okay radical Tsc shmoop er's Here we go I got

00:06

another question for you What value when cubed is equal

00:10

to negative to sixteen times x to the fifth So

00:17

how do we get there How do we get to

00:19

the cube root of this thing Well we separate the

00:21

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

00:24

got the cube root of negative to sixty next to

00:26

the fifth which is the same as the cube root

00:29

of negative one times cube root of to sixteen You

00:32

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

00:36

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

00:38

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

00:41

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

00:44

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

00:47

cube roots Slow and steady wins The race was going

00:49

to come one at a time Here we go Cube

00:51

root of negative one is negative one right Because negative

00:54

one two The third powers Negative one All right Once

00:56

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

00:58

of to sixteen Start by finding the prime factors of

01:02

two sixteen there and so whole lot of threes And

01:04

you know this because you could add two plus one

01:06

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

01:10

by three So you know three is going to be

01:12

one of those factors right Well to do so we

01:14

keep dividing out Smalls primes is possible Is shown here

01:18

we got two Sixteen equals two times one Oh eh

01:20

with vehicles two times two times fifty for which equals

01:23

two times two times two two twenty seven which equals

01:26

all this stuff right here at the end of the

01:28

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

01:31

we separate the factors and that allows us to take

01:34

the cube roots here So cube root of to sixteen

01:37

is the cube root of two to the third times

01:40

three to the third which is same as the cube

01:43

root of two to the third which is just too

01:46

in the cube root of three to the third which

01:48

is just three So the freakin answer is six You

01:50

could have gotten there by knowing that six times six

01:53

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

01:56

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

01:58

see that a lot of tests So you may I

01:59

just want to kind of note that in your brain

02:01

All right well specifically then we go to take the

02:04

cube root of x to the fifth by factoring out

02:06

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

02:08

the three plus two which is same as x to

02:11

the third times x to the squared or to the

02:13

second power there orjust x squared So once again separate

02:16

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

02:18

the cube root of exit third times x squared that

02:22

gives us the cube root of x cubed times the

02:24

cube root of x squared which equals x times the

02:27

cube root of x squared right there So we found

02:30

each of the three cube roots that we originally set

02:33

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

02:35

Put them all together and get your simplify on right

02:38

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

02:42

to sixteen there times cube root of x fifth is

02:44

the same as native One time six times acts times

02:48

cube root of x squared which same as negative six

02:51

x times the cube root of x squared wow that

02:54

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

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