Square root of ANY number instantly - shortcut math. - By tecmath
Transcript
| 00:01 | get a welcome with Tech Math channel . What we're | |
| 00:02 | gonna be having a look at in this video is | |
| 00:04 | how to work out the square root of any number | |
| 00:07 | fairly instantly to I mean , they don't have to | |
| 00:09 | be perfect squares either . Okay , so I'll give | |
| 00:13 | an example of this . Um , what is the | |
| 00:15 | square root Of 87 now ? This does not have | |
| 00:19 | a perfect square . Okay , so how fast can | |
| 00:21 | you work this out ? Okay . three seconds . | |
| 00:24 | Yeah . You should be able to work it out | |
| 00:25 | on our now , the answer that by the way | |
| 00:27 | was 9.33 and I'm gonna show you how to work | |
| 00:30 | this sort of thing out really , really quickly . | |
| 00:32 | So if you got that , congratulations . If you | |
| 00:34 | didn't you lucky , lucky person , I'm gonna show | |
| 00:36 | you right now how to do it . So just | |
| 00:38 | a couple things before I start , this does require | |
| 00:41 | that you will have a bit of a working knowledge | |
| 00:43 | with perfect squares . What do I mean by that | |
| 00:45 | ? So that , you know , you know , | |
| 00:47 | it's a six by six . Is 36 square at | |
| 00:49 | 2 36 . Is uh six . Yes or just | |
| 00:54 | those basic ones to start off with . Um Also | |
| 00:57 | this is fairly accurate but not 100% accurate . You'll | |
| 01:00 | see this , it gets pretty close . Um Not | |
| 01:02 | really really close , but it doesn't get 100% close | |
| 01:05 | . Okay . So it's it's pretty good though . | |
| 01:08 | Now the way this works as follows . Okay , | |
| 01:10 | so the square root of 87 the first thing we | |
| 01:13 | do to work these out is we look for the | |
| 01:16 | perfect closest perfect square below 87 . Okay . This | |
| 01:21 | well the closest perfect square root I guess before 87 | |
| 01:24 | . So we're looking The square root of 81 Is | |
| 01:28 | equal to nine . Okay , so that firms forms | |
| 01:31 | the whole number part of our answer . Okay , | |
| 01:34 | that's the first part is three parts . What we're | |
| 01:35 | gonna be doing ? The second part is we're gonna | |
| 01:37 | look at the difference between these two , numbers 87 | |
| 01:40 | and 81 . Okay , so the difference between 87 | |
| 01:44 | and 81 is six . So we're gonna put this | |
| 01:49 | There's a six . Okay , I'm going to put | |
| 01:51 | this over now . We're gonna do is get this | |
| 01:54 | number here . Whole number square . Uh And what | |
| 01:57 | we're gonna do is we are going to double it | |
| 02:01 | . I don't and that's our answer . Okay ? | |
| 02:03 | So this is equal to nine and 6 , 18 | |
| 02:05 | 9 and a third . Which is equal to well | |
| 02:08 | , put this in red 9.33 . How accurate is | |
| 02:12 | this ? I'll tell you the actual answer of the | |
| 02:15 | square root of 87 9 . Um I can tell | |
| 02:17 | you is in fact 9.9 point 3 to 7 . | |
| 02:24 | Okay , so look , we round up would actually | |
| 02:26 | get 9.33 , but it's pretty close . Right ? | |
| 02:29 | I'm pretty sure you'll agree this is really , really | |
| 02:32 | , you know , quite close . So you're just | |
| 02:34 | gonna go through those steps . Okay ? You look | |
| 02:35 | for the perfect square uh Oh , the square root | |
| 02:38 | below it . Uh That's your whole number . Answer | |
| 02:41 | . Look for the difference and then we're gonna double | |
| 02:43 | that answer uh to get this party . Okay ? | |
| 02:46 | We'll go through another couple of these . All right | |
| 02:48 | . All right , So did you like that ? | |
| 02:51 | I'll rub that out . We'll go through a bunch | |
| 02:53 | of examples . I'll tell you what , I'll go | |
| 02:54 | through a couple of examples and then I'll give you | |
| 02:57 | uh something to do . So what about the square | |
| 02:59 | root of 39 ? Give a couple of seconds to | |
| 03:04 | work that out . Yeah . Okay , you can | |
| 03:08 | even positive you want but you know , see how | |
| 03:10 | you go . Okay , so you probably know that | |
| 03:13 | square at 36 six . Okay . The difference between | |
| 03:19 | these 39 and 36 is three And double six is | |
| 03:24 | 12 . So where to is six and 3/12 which | |
| 03:28 | is six and a quarter which is 6.25 Okay . | |
| 03:33 | Uh the actual answer by the way is 6.24 , | |
| 03:37 | so we're not too far off . Okay again really | |
| 03:41 | really close . How do you go with that ? | |
| 03:43 | Good ? If you need me to slow down you | |
| 03:46 | can always ask computer but probably the best thing you | |
| 03:48 | might want to do is maybe pause it or even | |
| 03:51 | replay things . If you have to think that can | |
| 03:53 | help a lot . Uh Okay what about the square | |
| 03:56 | root of what about the square root ? Okay . | |
| 04:00 | An easy one . Square at a 12 . Okay | |
| 04:03 | and then the square root of 12 . You should | |
| 04:05 | be able to work that out because Yeah , the | |
| 04:08 | square of nine is equal to three . Difference between | |
| 04:13 | nine and 12 is three And a double of this | |
| 04:17 | through here is six . So this is three and | |
| 04:21 | 36 which is 3.5 , which is 3.5 . Now | |
| 04:24 | , what is the actual square root of 12 ? | |
| 04:28 | The actual square root of 12 is 3.46 Okay , | |
| 04:34 | so we're not really that far off , are we | |
| 04:39 | ? Okay , I'll give you a few examples and | |
| 04:41 | see where you go . You can pause these up | |
| 04:43 | , you know , check it out . This is | |
| 04:46 | really , really simple once you get a bit of | |
| 04:48 | a hang of it . So the couple of ones | |
| 04:50 | I'll get you doing is the square root of about | |
| 04:53 | 27 . The square root of will go a bigger | |
| 04:58 | one for you guys . 138 . The square root | |
| 05:02 | of Um which one maybe ? What about 18 ? | |
| 05:10 | Okay . All right , pause the video . See | |
| 05:14 | here you go . The case of how did you | |
| 05:18 | go ? All right . We'll go through a few | |
| 05:20 | of these answers . The square root of 27 . | |
| 05:23 | So the square root of 27 , the next one | |
| 05:25 | below this is uh lost . That there . Have | |
| 05:28 | to find that back . I said pull that back | |
| 05:30 | . Very good . Uh square to this closest one | |
| 05:33 | is a square to 25 . Okay , So the | |
| 05:36 | square root of 25 . So the answer is going | |
| 05:39 | to be a five . The difference between these is | |
| 05:42 | two and double five is 10 . So this You | |
| 05:45 | probably need the answer of 5.2 . All right . | |
| 05:50 | The actual answer of the square of 20 . Uh | |
| 05:53 | the actual answers square of 27 by the way , | |
| 05:55 | is 5.19 . Okay . 196 . As you go | |
| 05:59 | that good . Or I'll do this in a different | |
| 06:02 | color . Well , that's squared of 138 . Okay | |
| 06:05 | . Did go a bit higher this time , but | |
| 06:07 | 11 11th Are 121 . So the square root of | |
| 06:10 | 121 . Okay , we're going to be getting 11 | |
| 06:14 | is the answer there ? The difference between these two | |
| 06:18 | is 17 . The double of 11 is 22 . | |
| 06:22 | Okay . This fraction is a little bit harder . | |
| 06:24 | You can sort of look and go , this is | |
| 06:25 | almost 15 out of 20 . This is almost 11.75 | |
| 06:31 | . Okay , if you want to get it exactly | |
| 06:32 | and you could really work it out , you know | |
| 06:34 | ? But 11.977 is exactly the work this , but | |
| 06:37 | 11.75 is a good approximation . So and finally enough | |
| 06:41 | . 11.75 is the exact square root . So I'll | |
| 06:45 | put in If you were to work out this , | |
| 06:47 | it would be 11 .77 . But the exact square | |
| 06:50 | root is 11.75 , so not bad . Okay . | |
| 06:56 | Last one , lucky . Last what about squared of | |
| 07:00 | 18 ? Okay , then , one below this is | |
| 07:02 | the square root of mental blank for a minute squared | |
| 07:06 | of 16 , which is four . That happens , | |
| 07:09 | doesn't it ? Um the uh the difference between these | |
| 07:11 | guys is to and a double of four is eight | |
| 07:17 | . So this is 4.25 Okay . 4.25 which is | |
| 07:23 | clearly close to the actual square root , which is | |
| 07:26 | a squared of 18 is 4.24 So I do that | |
| 07:31 | one right ? The difference between these guys , yeah | |
| 07:33 | , I did do that right now . I'm living | |
| 07:35 | in a funny little land . Okay . Oh , | |
| 07:37 | sudden , second guess myself . That's pretty easy . | |
| 07:40 | Right ? So hopefully you like this trick and hopefully | |
| 07:43 | I didn't make too many mistakes . I do those | |
| 07:45 | occasionally . Like we all do . Uh , of | |
| 07:47 | course , if I make mistakes , get on their | |
| 07:49 | flame me tell me off . All right , Anyway | |
| 07:53 | , I hope you enjoyed that trick . It's really | |
| 07:55 | great to make a video for you guys . See | |
| 07:58 | you next time I see you . |
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