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如何心算开立方?

How To Calculate Cube Roots In Your Head

Hi, this is Presh Talwalkar.
大家好 我是Press Talwalkar
In this video I’m going to teach you how you can calculate cube roots (∛) in your head.
在这个视频中我将教会你们如何心算立方根
Why would you ever want to do this?
你为什么会想要算立方根呢?
The Education Secretary Nicky Morgan was recently on TV and put
教学部长Nicky Morgan最近上了电视
on the hot seat.
并且处于尴尬的境地
She was asked by a ten-year-old the question,
一个10岁的小朋友问了她一个问题
“What Is the cube root of 125?”
“125的立方根是多少?”
She refused to answer any math questions on TV and I understand that.
我理解她在电视节目中拒绝任何数学问题
But if she knew the trick in this video,
但是如果她从这个视频中学到了技巧
she could have answered it very
她就很快的回答出来
quickly and done many more math problems.
并且回答更多的数学问题
So to do the trick,
那么想要做到这点
you first have to memorize the cubes of each number from 1 to 10.
首先你得记住1到10的立方
The cube of a number is the number multiplied by itself three times.
数字的三次方是这个数字本身乘三次
So the cube of 1 is still 1.
所以1的立方仍然是1
The cube of 2 is 8.
2的立方是8
The cube of 3 is 27.
3的立方是27
And I’m going to keep writing the cubes of each number.
我继续写每个数字的立方
So you may know some of these. Otherwise,
可能你知道一些立方
to do this trick you’ll have to memorize these ten numbers.
不然的话你就需要记住这十个数字
Now once we’ve written down these cubes, I
我们已经写下了这十个立方数
want you to focus on the very last digit
我希望你们关注
of the number of the cube.
表中的立方的最后一位数字
So what’s important is that each of these 10 numbers end
所以重要的是
in a different last digit.
这十个数字个位都不同
And that’ll be very important to doing this trick.
这对我们掌握这个技巧十分重要
So this will be another thing you have to memorize.
这是你需要记住的另一个东西
When you memorize these 10 digits, you should also remember the last digit.
当你记住这十个数字时 请记住它们的个位
So an easy way to remember this is that
对于数字1 4 5 6 9 0
for the numbers 1, 4, 5, 6, 9, and 0,
记住它们的个位比较简单
the last digit is the same as the numbers.
它们立方的个位与数字本身相同
And for the numbers 2 and 8,
对于数字2与8和3与7
and 3 and 7, the last digit flips.
它们立方的个位数相互交换
So the last digit for 2 is 8,
所以2的立方的个位数是8
and the last digit for 3 is 7 and vice versa.
3和7的立方的个位数亦是如此
So let’s do the trick.
让我们来开始练习一下
What’s the cube root of 39,304?
39304的立方根是什么?
The first thing I want you to do is look at the last digit.
第一件事是看它的个位数
The last digit of 39,304 is 4,
39304的个位数是4
which we’re going to put in a box.
我们把它圈出来
So we look up 4 in the last digit,
它的个位数字是4
and that corresponds to the number 4.
所以它对应的数字也是4
So we write down the number 4.
所以我们写下数字4
The next step is we ignore the last three digits of our number.
下一步我们要忽略最后的三位数字
So in 39,304, we’re going to just ignore the 304.
对于39304来说 我们要忽略304
And now we want to find the closest cube without going over.
现在我们要找到最接近它的立方数 不能超过它
So 39 is between 27 and 64,
39介于27和64中间
so it’s actually closest to 27 without going over,
实际上它更接近27 不超过它
which means it’s closest to the cube of 3.
这意味着它更接近3的立方
And that gives us the other part of our answer, which is 3.
这给了我们答案的另一部分 那就是3
So here we have it,
那我们就得到了它的答案
we put the numbers together and 34 Is the cube root of 39,304.
我们把数字拼在一起得到34 就是它的立方根
So why would this ever be useful?
所以这个什么时候能用呢?
So here’s a trick you can do.
你可以玩一个小游戏
Ask someone to pick a number from 1 to 100,
让一个人从1到100中选一个数字
and just think about it secretly, don’t have them tell you the number.
并且记在心里 不要告诉别人
Have them cube the number on a calculator.
让他们在计算器中计算它的立方
And once they cube the number, they tell you the cube
当他们计算好后 告诉你立方是多少
and you instantly can tell them the cube root
利用我们的技巧和这个表格
by using this table and using the trick.
你可以立即告诉他们这个数字的立方根
So let’s imagine they tell you the number is 636,056.
假设他们告诉你的数字是636056
So we look at the last digit, which is 6,
它的个位数是6
and when the last digit is 6, that corresponds to the number 6.
当个位数是6时 它对应的就是数字6
And then we look at the, we ignore the last three digits and we look at 636.
接着我们忽略最后三个数字 直接看636
That’s between the cubes of 8 and 9, so we put 8.
这介于8和9的立方之间 所以我们写上8
And therefore, the cube root is 86.
因此它的立方根为86
So once you get used, once you’ve memorized this table,
一旦你记熟了这个表格
you’ll actually be able to do this very quickly.
你算起来会非常快
Let’s do another example.
让我们再举一个例子
185,193 We look at the last digit of 3.
对于185193我们看它的个位数3
That corresponds to the number 7 because 3 and 7 flip.
这对应着数字7 因为3和7相互交换
Then we ignore the last three digits and we look at 185.
接着我们忽略最后三位数并且看185
And that’s closest to the cube of 5 without going over.
毫无疑问这数字最接近5的立方 不超过它
So that gives us the answer of 57.
所以答案是57
So it’s a pretty neat trick.
这是一个非常巧妙的技巧
And if you want to know how this works, you can click through.
如果你想知道它的原理 可以访问网站
I’ve made a short video which gives a math proof.
我录了视频来演示数学推导过程
If you like this video, please subscribe to my channel.
如果你喜欢这个视频 你可以订阅我们的频道
You can support me on Patreon to get exclusive rewards.
你可以在Patreon上支持我们 将会得到定制礼品
Catch me on my blog MindYourDecisions, on Twitter @preshtalwalkar.
在博客和推特上关注我们
And you can get my books listed on my website.
并且你可以在网站上找到我的书

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视频概述

本视频帮助你更快的求出立方根

听录译者

收集自网络

翻译译者

吴亦宸

审核员

审核员BZ

视频来源

https://www.youtube.com/watch?v=Ds8ijPsg26g

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