“You’ll find many books which say that mathematics is fun, but remember, it can also be ‘gun’!” This is what my mathematics teacher says sometimes. But for the time being, let’s keep the ‘gun’ part out.
Picture the following scene – You’re chatting with your friends at school and suddenly you announce, “Tell me to square any number and I’ll do it in a minute without pen and paper.”
You’re friends are all very excited and one of them says, “Okay! Let’s see how smart you are. Square 56.”
You look at him for five seconds with a “l-didn’t-expect-that-easy” smile on your lips and say, “three, one, three-six.”
They do it on the calculator and it’s correct!
He must have known it by chance. He’s bluffing,” says someone. “I’ll believe you’re a super genius if you can do 146.”
You knit your brows, and after half-a-minute, say, “two, one, three, one-six.”
It’s right again! Your friends ask, “How do you do it?” You smile sarcastically and say, “It’s plain and simple multiplication. A genius does it a bit faster than normal people- that’s it!”
Now wouldn’t that be great? It’s easy. And, as you’ve already guessed, it’s not only a genius’ mind that can do it.” Here’s how you do it –
Suppose, the number they give you is ’48’. You know the square of 50 is 2500 and that the difference of your number from 50 is 2. All you’ve got to do is multiply 2 by 100, subtract it from 2500 and square the square of 2 to the result- you’ve got 48^2=2304!
It’s that easy! And if the number is greater than 50, say 52, then just add the difference multiplies by 100, (2*100, in this case) to 2500 and then add the square of the difference to the answer. That’s it! 52^2=2704.
Does it seem a bit complicated? Well, it won’t after you’ve done it once yourself. Following is the mathematical calculation for 52^2.
52^2-50^2+(52-50)*100+(52-50)^2
=2500+200+2^2=2704
But what if they give you ’98’ to square? You’ll just have to use the number 100 as you’ve used 50 earlier and you’ve got to multiply the difference by 200 and not 100.
So, 98^2=100^2-(100-98)*200+(100-98)^2
=10000-400+2-9604
In the same way, for numbers near 150, use it with 300 and so on. But, if you really want to impress your friends and use this technique in your exams, you must memorise the squares of numbers from 1 to 25.
And before they give you a number to work on, don’t forget to say, “But of course, don’t give me crazy big numbers like 251^2 because it’s hard work. Abut that doesn’t mean I can’t do 251^2!” Then do it and surprise them!