The Maths and Science Thread - Collection of Problems and Facts

[Dipak]

Fantastic work there mate. You should even consider multiplication by 25 i.e. multiply by 100 and divide by 4.

 

[Varun]

Fantastic work there mate. You should even consider multiplication by 25 i.e. multiply by 100 and divide by 4.

Yeah, that as well.

 

[Chewie]

Those are all stuff I figured out myself in primary school...

 

[Varun]

I know that one is pretty much obvious, , and I've mentioned it 'easy' everywhere in the blog as well and that most (or many) people might know it as well, but couldn't find anything better to start the blog. More, better stuff coming, as I said earlier.

And surprisingly, on average, as I have noticed, people don't know about this stuff.




(and yeah, I figured them out in primary school, but that's not the case with the more difficult ones, like calculating the square of any number mentally. )

 

[Dipak]

like calculating the square of any number mentally. )

Yep it's like if you wanna find the square of n then add (n*2)-1 to the square of the previous number, am I right? Well I don't know if it works for all nos. but just a small self devised method which I observed 2 yrs ago.

 

[Varun]

That one's only valid for consecutive numbers.

 

[Dipak]

That one's only valid for consecutive numbers.

yeah i know that

 

[AbhishekS]

During school days while studying History some day, I was feeling bored and was having fun with numbers, when I observed something cool. I don't know whether the trick is a known one or not, and so I will share it here.

It's a trick to get the square of two digit numbers. It's hard to explain it via text on a general basis, and so I'll explain it using an example.

Step 1: If we want the square of 57, the digit at the units place of the square will be 9.
Reason: The square of the second digit (7) is 49, and so we take out 9 from it and carry 4 in the next step.

Step 2: Now, we multiple 5 by 7 (as the number is 57) and then multiply the product by 2 (we always multiply by 2). The answer comes as (35*2) 70. We carried 4 from the previous step, so we add up 4 to this and we get (70+4) 74. Again, we just take out 4 from 74 and carry 7 in the next step.
The answer till now is _49.

Step 3: Now we take the square of 5 (earlier we took the square of 7, now of 5 as the number which we are squaring is 57). The square is 25, and we add up 7 to it as we are carrying it from the previous step. The answer comes to (25+7) 32. We write it besides 49, and so finally the square of 57 turns out as 3249.

While reading it may seem to be a huge process which consumes a lot of time, but when you practically try it, it's too simple and the square is obtained within 5-7 seconds. I always use this trick if I need to find the square of a 2 digit number.


Few Examples

1. To take the square of 32.

After 1st step, we get _ _4 (nothing carried)
After 2nd step, we get _24 (carrying 1)
After 3rd step, we get the answer as 1024.


2. To take the square of 86.

After 1st step, we get _ _ 6 (carrying 3)
After 2nd step, we get _96 (carrying 9)
After 3rd step, we get the answer as 7396.

---

The entire credit of the trick goes to me as I never heard or read about it and discovered it while I was bored of studying History.

Try it, its very useful.

 

[Chewie]

That works because of this:
(10a+b)^2
100a^2+20ab+b^2

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It's basically exactly what you've done except explained in words

 

[AbhishekS]

That works because of this:
(10a+b)^2
100a^2+20ab+b^2

Yeah, but I don't prefer splitting the numbers and then squaring them. For some reasons, I am very comfortable with the method I mentioned, probably because I have been using it for several years now.

 

[Chewie]

Same thing really :/

 

[AbhishekS]

Same thing really :/

Yeah, its EXACTLY the same, but when trying to find the square mentally, the method which I mentioned works perfectly. I feel that the splitting method has a high risk of yielding silly errors when tried mentally.

 

[Varun]

There is an even easier method.

Great work on that as well though.

 

[Varun]

Top 10 Lists - Listverse

Brilliant website for someone who's looking to spend his time reading something intriguing.

 

[AbhishekS]

There is an even easier method.

Great work on that as well though.

For me, nothing can get easier than the method I posted. Possibly because I have been using it for years and have become quite used to it now.

And thanks for the compliment.