SIMON PAMPENA: So, 2 × 2 × 2 × 2 × 2 ...
OK, two multiplied by itself five times is 32.
So the opposite of that, is a question: What number multiplied by itself five times gives you 32?
And the way you express that, is that you go, is 32 to the fifth.
That's the fifth root.
And that happens to be 2.
So, because in mathematics, there's some beautiful patterns, there's actually a way
that you can work out the fifth root of very large numbers in your head very quickly.
And you don't have to use a lot of computing power, brain power.
So, Brady, if you take any double digit number you like, and multiply by itself
5 times
and you tell me that number, in English, from left to right,
and I write it down, I will be able to tell you what your original number was.
OK.
OK, you got a number?
BRADY HARAN: Yeah. SIMON PAMPENA: Is it big?
BRADY HARAN: Yeah, it's big. You ready?
It's 79 million — PAMPENA: Wait a minute. —
PAMPENA: 79 million. — HARAN: 235 thousand.
PAMPENA: 235 thousand.
HARAN: 168.
PAMPENA: 168. (the number was 79,235,168)
So your number is 38?
HARAN: Well yes it is.
PAMPENA: It is? — HARAN: It is.
PAMPENA: OK. HARAN: Very good. [chuckles]
PAMPENA: How did I do it so quickly?
I'm genius. [chuckles]
HARAN: We're gonna... [Both laugh.]
PAMPENA: Well, obviously not. I did it because there's a pattern in the numbers.
OK? So... it's actually to do with a wonderful mathematician, Euler. This is Euler's Theorem.
And I'm actually not going to write down what Euler's theorem is.
I'm actually going to show you a result from Euler's Theorem.
For any number, a.
a^5, is equal to 10m+a for some m.
So you can get that from Euler's Theorem.
Now that's not the theorem itself, but I just want to cut to the chase here.
So, what is, let's actually do an example. So let's do 47^5.
Okay, so 47^5 — actually, we can write it as 22,934,496
times 10, + 47.
So, if we expand this out, a number *10, you put a 0 on the end, right?
So it goes 229,344,960
+, and if we do what we do in primary school,
+47, look what you've got at the end.
0+7=7. So what that means is, any number multiples by itself 5 times, the last digit
doesn't change.
So for me to know what the last digit of your number was, I just have to wait to hear you say it.
And then I write it down.
OK?
The first digit? That's a bit harder.
The first digit, you've got to memorize all the powers of the 10s, ^5.
So, that's 100,000.
20^5... is 3 million.
30^5. There's that.
40^5 is that.
50^5 is that.
60^5. That.
80^5 is, uhh...
And 90^5.
Now the interesting point here, is that these numbers, you can notice...
10-1, 20-2, 30-3, 40-4. See that? These numbers are all the same.
Those — 5, 6 — They're the same as that number there.
And the reason why is because of that if you can think about it.
So when you said the number, Brady — So you said 79 million — automatically I thought 79 million
So I know that's between 30^5, and 40^5. OK? —
And then you went on and did 235 thousand —
I had kind of tuned out at that stage. I wasn't really paying attention. Don't take it personally.
I was just waiting for you to hist the jackpot at the end.
So if you have someone who reads out the number, who's an accountant or something, or an engineer —
there's an engineer —
who just kinds of gives you a rough estimate, you're stuffed.
HARAN: That's still a big ask to memorize all that.
PAMPENA: Is it?
It didn't take me that long.
You just have a feel for the numbers.
It doesn't have to be that precise. — HARAN: You just need to memorize the — PAMPENA: You just need to
know that it's anything between 3,000,000 and 24,000,000. You know, you don't have to be that precise.
Anything that's greater than 100,000,000 and — You know, when I go to schools, if I do this for school kids, they
always pick something in the 90s. But the 90s is so easy, because it's anything greater than 6,000,000,000.
So if they go, "8,000,000!!", you just go, "9."
And you just wait until they say the thing at the end.
The hardest ones are actually down here.
Down here.
And it's actually hard in the transition.
I had trouble quite a bit. Believe it or not, a lot kids love to do 69^5. And that one was hard,
because it crossed over from 777 million up to 1.7 billion.
That was a bit hard.
But I got used to it.