- Let'ssee if we can calculate the fifth root that 32. So, like always, pause thevideo and also see if you can figure this the end on her own. So, let's simply remindourselves what a fifth root is. So, if x is equal to the 5th root that 32, that's the same thing as saying x to the fifth power is equal to 32. So, we have actually to discover some number where, if friend take 5 of themand multiply them together, you'd gain 32. So, there is a couple ofways to method this. Especially when you're taking care of these really high order roots here. So, let me rewrite thefifth source of 32 here. One method is you could try to variable 32 and also see space there factorsthat show up five times? So, 32 you could immediatelyrecognize is an even number. So, it's gonna be divisible by two. It's two times 16. 16 is two times eight. Eight is two times four. Four is two times two. So, in this case, doing the factoring an approach worked the end well. 'Cause we watch that this is 2 times two timestwo times 2 times 2 or 2 to the 5th power. You can rewrite this together the fifth root of 2 to the 5th power, i beg your pardon is, of course,going come be equal to two. Two to the fifth power is 32. Now, let's do one more one. It's gonna be a tiny bit harder. Let's say us wanna takethe 5th root the 243. So, now, a much, much bigger number. So, there's a couple of ways to carry out this. One, you could try the factoring. Although, that's gonna it is in harder currently that it's a larger number. Or you might do a littlebit of trial and also error. Doing greater roots there is no the assist of some form of calculator or miscellaneous is a small bit more complicated. So, here, if we wanted todo the factoring technique. We might say, alright,it's not divisible by two. I favor to start with thesmallest possible factor. So, it's not divisible by two. Is the divisible by three? and you can be familiar with the test to view if other is divisible through three. You add up the digits and see if that sum of the number is divisible by three. So, if ns were to taketwo plus four plus three, the is same to nine. And so that is divisible by three. So, this is going to beequal to three times... Let's see three goes into240 80 times and also then one. So, 81 times. And also so, 81 is likewise divisible by three. I have actually a sense of where this is walk now. It's three times 27,which is three times nine. Which is 3 times three. So, using the factoring method, we're able to check out that threeto the fifth power is 243. So, the fifth root of243 is equal to three. Now, another means thatyou could have excellent it is a little bit that trial and also error. We currently know.. Well, we know that one to the fifth power is simply going to be one. We know that two to the fifth power... We simply calculated that. That's 32. Well, us now know whatthree to the fifth is. Let's say we're just trying come zoom in on it a little bit. So, let's say, if you want to watch what 4 to the 5th is. Well, that would be four times 4 times 4 times 4 times four. So, let's see, this is walk to be 16. 16 times four is 64. Times four is 256. And also then, the times four... And I just occur to know this. Yet you might wanna execute it by hand. This is 1024. So, if you're acquisition the cube root of 243, you're speak what come the fifth power... Something to the fifthpower is equal to 243. And, if you have actually a feeling that it's walking to be an essence solution, if friend think it's going to be something prefer a 2 or a three, well, then, 3 is probablygoing to it is in a great guess here. If the possible answersare gonna it is in decimals, then it's going to bea lot much more complicated. Yet that's one more way.

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Say, hey, perhaps I'll shot a three. And, if you try outthree, friend would acquire 243.