How to Square Numbers Quickly
In this post we are going to look at how to square any two digit numbers.
[private]Firstly, to square a number means to multiply that number by itself.
So 27² means 27 X 27
When squaring any number we need to either work up or work down from a BASE number. We acknowledge that a base number is a whole number closest to the number we want to multiply. So taking the above example of 27² we would use the base number of 30.
So, the first rule we need to do is find the base number.
Next rule, we need to count how far away the number to be squared is from the base.
Keeping with the above example, we know that 27 is three away from 30.
So now we lay out the calculation like so:
As you can see, we’ve also added 24 to the image. You see, when we add three to the 27 to get 30, we also need to take 3 away from 27 to balance the sum.
You would do this for all sums you are squaring using this method.
The next step is real simple We need to multiply 24 X 30… Don’t worry! It’s easy and here’s why.
We don’t really need to multiply 30 X 24 or 24 X 30 (same thing), all we need to do is multiply 24 X 3 and then add a 0 to the end.
I would probably do 24 X 3 this way:
Add one to 24 giving 25, then 25 X 3 = 75.
Take away the three 1’s giving us 72.
So 24 X 3 = 72
Now we can add back the 0 and we find that 24 X 30 = 720.
The sum is almost complete.
Look back at the image again:
Notice the +3 and -3. Forget about any – values and just multiply 3 X 3 giving 9.
Add this to 720 and we find that
27² = 729
Don’t get overwhelmed by it from that one example. It really is a pussycat once you’ve grasped how to do it
Let’s try another example, and this time it’s going to be an even bigger number than before, but it certainly doesn’t make it any more difficult.
Let’s say 56²
Lay out the sum again just like in the image before:
So, just like before we need to multiply 52 X 60 but all we really need to do here is multiply 52 X 6 and add a 0 on the end.
52 X 6 is easier if you do 50 X 6 which is 300 then 2 X 6 = 12 so
52 X 6 = 312
Add the 0 on the end and 52 X 60 = 3120
Take the +4 and -4 and just multiply the numbers 4 X 4 giving 16. Add it to the end of 3120 and we get
56² = 3136
By using this technique I hope you can see that those big calculations aren’t that difficult once you have a good system in place.[/private]
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