Full transcript
Introduction
0:03What is the square root of 55?
0:06Now we know that 55 is not a perfect
0:10square which means the answer will not
0:12be an integer.
0:14In many exams we are not allowed to use
0:16a calculator.
0:18What's the solution then? The best way
0:21to go about it is approximation.
approximating roots
0:25All we need to do is think of the two
0:27perfect squares 55 lies between. It lies
0:30between 49 which is 7 squared and 64
0:35which is 8 squared. That gives us a big
0:38big hint. Route 55 lies between roo<unk>
0:4249 and<unk> 64. It lies between 7 and 8.
0:47But that's not enough. What do we do
0:50now? Maybe we can find out how far 55 is
0:54from 49 relative to how far 64 is from
0:5849.
1:00To know how far 64 is from 49, we find
1:04the difference between 64 and 49. That
1:08equals 15. And to know how far 55 is
1:11from 49, we find the difference between
1:1455 and 49. That is 6. Now 6 over 15 will
1:20tell us how far the answer is from 7.
1:246 over 15 is 2 over 5 which is 0.4.
1:29So<unk> 55 will approximately equal 7.4.
1:34First we found out the perfect squares
1:3655 lies between. Then we found out how
1:40far 55 is from 49 relative to how far 64
1:44is from 49. If you use the calculator,
1:48you would get the value as 7.416,
1:52which is very close to 7.4.
1:55Okay, good. Now try finding the square
approximating square root (example)
1:58root of 210 in the same way.
2:06Route 210 lies between roo<unk> 196 and
2:11roo<unk> 225.
2:14196 is 14 squared and 225 is 15 squared.
2:21R<unk> 210 lies between 14 and 15.
2:25Now we just need to find out two things.
2:28How far 225 and 210 are from 196?
2:35225 - 196 gives us 29 and 210 - 196
2:44gives us 14.
2:4614 / 29 is what we are interested in. 14
2:50/ 28 would be exactly half. As the
2:54denominator is slightly higher than 28,
2:57this fraction would be slightly lesser
2:59than half. Close to 0.48 or 0.49. 49. We
3:05can say that<unk> 210 will approximately
3:08equal 14.48.
3:10[Music]