1
00:00:01,556 --> 00:00:08,452
we are after to find the cube root of -343 or another way to think about it is some number that when

2
00:00:08,452 --> 00:00:13,189
I multiply itself by three times I am going to get -343

3
00:00:13,189 --> 00:00:22,384
or another way to view it it is the same thing as -343 to the 1/3 power and the best way to do this is

4
00:00:22,384 --> 00:00:29,443
really just try to factor this out so the first thing that we could do is..so let me just factor -343

5
00:00:29,443 --> 00:00:37,918
the first thing I would like to do factor is -1 so it is same thing as -1 times 343 and lets just think about this

6
00:00:37,918 --> 00:00:40,403
is it divisible by 2? no

7
00:00:40,403 --> 00:00:47,531
is it divisible by 3? the digits do not add up to a multiple of 3 they add up to 10 so it is not divisible by 3

8
00:00:47,531 --> 00:00:50,155
it is not divisible by 4 since its odd

9
00:00:50,155 --> 00:00:53,267
not divisible by 5 since it does not end with 5 or 0

10
00:00:53,267 --> 00:00:56,448
it is not divisible by 6 since it is not divisible by 2 or 3

11
00:00:56,448 --> 00:00:59,536
is it divisible by 7 let's check this out

12
00:00:59,536 --> 00:01:03,344
7 goes into 343

13
00:01:03,344 --> 00:01:09,544
7 goes into 34 four times 4 times 7 is 28

14
00:01:09,544 --> 00:01:14,211
34-28 is going to be 6 bring down 3

15
00:01:14,211 --> 00:01:18,460
7 goes into 63 exactly 9 times

16
00:01:18,460 --> 00:01:19,482
so then we end up

17
00:01:19,482 --> 00:01:22,617
9 times 7 is 63 no remainder

18
00:01:22,617 --> 00:01:25,635
so this is going to be 7 times 49

19
00:01:25,635 --> 00:01:30,210
now we know that 49 is samething as 7 times 7 so how can we

20
00:01:30,210 --> 00:01:38,337
rewrite this it is the same thing as taking ... it is the same thing as taking the cube root...the cube root of

21
00:01:38,337 --> 00:01:47,276
-1 of -1 times 7 times 7 times 7 which is the same thing

22
00:01:47,276 --> 00:01:56,355
as the cube root of -1 times the cube root of 7 times 7 times 7

23
00:01:56,355 --> 00:02:06,456
now what is the cube root of -1 well -1 times itself three times is -1 so this right here is -1

24
00:02:06,456 --> 00:02:10,194
you could verify -1 times -1 times -1 is indeed -1

25
00:02:10,194 --> 00:02:12,075
this becomes positive 1

26
00:02:12,075 --> 00:02:14,653
multiplied by -1 again you get -1

27
00:02:14,653 --> 00:02:16,742
so this is -1

28
00:02:16,742 --> 00:02:21,804
and then this over here the cube root of 7 times 7 times 7 well that's just going to be 7

29
00:02:21,804 --> 00:02:26,262
7 multiplied by itself three times gives us 7 times 7 times 7

30
00:02:26,262 --> 00:02:28,329
or 343

31
00:02:28,329 --> 00:02:30,674
which is going to -1 times 7 which is the same thing as -7

32
00:02:30,674 --> 99:59:59,999
so our answer is -7 and we are done