Oh, by the Gods ...

[fiat_knox]

I can square any two digit number in my head.

I never used to be able to do that before.

The easiest to multiply are the numbers that end in 5: 45² = 2025, 65² = 4225.

I squared 317 just now, and came up with 100,489.

In my head.

In ten seconds.

Until just now, I have never multiplied 317 by anything, let alone itself.

...



...

I still err on occasion. I still have brainfarts when I start thinking of the magnitude of what I am doing instead of just doing it. And because I haven't had practice at this any bugger with a calculator can still beat me.

But ...

I can multiply 999,999,999,999,999,999,999 x 111,111,111,111,111,111,111 - and the result takes longer for me to write out than to calculate because I've worked it out already.

The result is

111,111,111,111,111,111,110,888,888,888,888,888,888,889

and I defy you to find a calculator with enough digits to work that one out! :0D

Comments

[thewingsofisis.livejournal.com]

The easiest to multiply are the numbers that end in 4: 45² = 2025, 65² = 4225.

Wait, what?

[fiat-knox.livejournal.com]

Yup. :) Want to know that particular secret? :D

[sandchigger.livejournal.com]

I think he (or she) was saying that both those numbers end in 5, not 4 as you wrote.

[fiat-knox.livejournal.com]

Hey, look at the big ugly spider over there! *points*

*retcon retcon retcon scribble scribble scribble*

Is that so? 0:)

[sandchigger.livejournal.com]

Ah, I see, yes. I appear to have been mistaken.

[thewingsofisis.livejournal.com]

I would love to know the secret of numbers that end in 4, but are 45 and 65. :)

[fiat-knox.livejournal.com]

Mea culpa. Consider that one of the brainfarts.

I said I could work out the math in my head. Didn't say I was any good at writing it down on paper or on screen ...

All The Fours

[fiat-knox.livejournal.com]

Okay, then, here's an example of squaring a two digit number ending in 4.

64² = ????

I'd know this anyway, from the old familiar progression of 1, 2, 4, 8, 16 ... but for the purpose of this exercise, I have never had to work out 64² in my life before.

64 x 64 ==> ((64 + 4) x (64 - 4)) + 4²

==> (68 x 60) + 16

==> (680 x 6) + 16

==> 4080 + 16

==> 4096.

Can you see how this process also works for 34 and 74 alike? :)

All The Fives

[fiat-knox.livejournal.com]

If you're squaring a two digit number ending in 5, it's even simpler and quicker.

Take the first digit. Multiply it by the next number above it.

Multiply by 100.

Add 25.

Try it with 15², 35², 75² and 85². :)