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#### 如何心算开立方？

Hi, this is Presh Talwalkar.

In this video I’m going to teach you how you can calculate cube roots (∛) in your head.

Why would you ever want to do this?

The Education Secretary Nicky Morgan was recently on TV and put

on the hot seat.

She was asked by a ten-year-old the question,

“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.

But if she knew the trick in this video,

she could have answered it very

quickly and done many more math problems.

So to do the trick,

you first have to memorize the cubes of each number from 1 to 10.

The cube of a number is the number multiplied by itself three times.

So the cube of 1 is still 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.

So you may know some of these. Otherwise,

to do this trick you’ll have to memorize these ten numbers.

Now once we’ve written down these cubes, I

want you to focus on the very last digit

of the number of the cube.

So what’s important is that each of these 10 numbers end

in a different last digit.

And that’ll be very important to doing this trick.

So this will be another thing you have to memorize.

When you memorize these 10 digits, you should also remember the last digit.

So an easy way to remember this is that

for the numbers 1, 4, 5, 6, 9, and 0,

the last digit is the same as the numbers.

And for the numbers 2 and 8,

and 3 and 7, the last digit flips.

So the last digit for 2 is 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.

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.

The last digit of 39,304 is 4,
39304的个位数是4
which we’re going to put in a box.

So we look up 4 in the last digit,

and that corresponds to the number 4.

So we write down the number 4.

The next step is we ignore the last three digits of our number.

So in 39,304, we’re going to just ignore the 304.

And now we want to find the closest cube without going over.

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,

which means it’s closest to the cube of 3.

And that gives us the other part of our answer, which is 3.

So here we have it,

we put the numbers together and 34 Is the cube root of 39,304.

So why would this ever be useful?

So here’s a trick you can do.

Ask someone to pick a number from 1 to 100,

and just think about it secretly, don’t have them tell you the number.

Have them cube the number on a calculator.

And once they cube the number, they tell you the cube

and you instantly can tell them the cube root

by using this table and using the trick.

So let’s imagine they tell you the number is 636,056.

So we look at the last digit, which is 6,

and when the last digit is 6, that corresponds to the number 6.

And then we look at the, we ignore the last three digits and we look at 636.

That’s between the cubes of 8 and 9, so we put 8.

And therefore, the cube root is 86.

So once you get used, once you’ve memorized this table,

you’ll actually be able to do this very quickly.

Let’s do another example.

185,193 We look at the last digit of 3.

That corresponds to the number 7 because 3 and 7 flip.

Then we ignore the last three digits and we look at 185.

And that’s closest to the cube of 5 without going over.

So that gives us the answer of 57.

So it’s a pretty neat trick.

And if you want to know how this works, you can click through.

I’ve made a short video which gives a math proof.

If you like this video, please subscribe to my channel.

You can support me on Patreon to get exclusive rewards.

Catch me on my blog MindYourDecisions, on Twitter @preshtalwalkar.

And you can get my books listed on my website.