Square Number: Some Tricks and Examples
In this post, we are going to learn some tricks or strategies for being capable of calculating a square number mentally.
What is a square number?
A square number or a number raised to the power of 2, is a number multiplied by the same number.
In those cases the multiplication is simple, but if we want to calculate 62² the multiplication is more complicated. This is why we are going to look at two tricks for finding the square of numbers in a much simpler way.
Square of a number that ends in 5
The steps to follow are:
- We remove the units ones place digit from the number, that is to say, we remove the 5.
- We multiply the number that remains by the number that comes after this number when counting.
- We add the number 25 on to the end of the result of the previous multiplication.
- We already have the result of taking the square of that number.
Let’s look at an example: 25²
- We take the number 25 and remove the 5. So only the 2 remains.
- We multiply the 2 by the number that follows it when counting (so 3) following number:
2 x 3 = 6
- After the 6 we add the number 25:
- We have already arrived at the result of the operation:
25² = 625
Another example: 405²
- We take the number 405 and remove the 5. We are left with 40.
- We multiply 40 by the number that follows it when counting (so 41) following number:
40 x 41 = 1,640
- We add 25 on to the end of the number:
- We have already arrived at the correct result:
Square of a number close to 50
Let’s consider the numbers close to 50: those that are between 41 and 59. For these numbers you calculate their square in the following manner:
- We subtract 25 from the number. This number will be the first two digits of the final result.
- We find the difference between 50 and the number.
- We square that difference and the result will be the last two digits of the final result.
Let’s look at an example: 47²
- We subtract 25 from the number. These will be the first two digits of the number.
47 – 25 = 22
- The difference between 50 and 47 is:
50 – 47 = 3
- We square the number 3:
3² = 9
The first two digits of the number are 22 and the last two digits are 09.
47² = 2,209
Let’s look at another example: 56²
- We subtract 25 from the number:
56 – 25 = 31
- We take the difference between the number and 50:
56 – 50 = 6
- We square the previous number:
6² = 36
Combining the first two digits and the last two digits we are left with:
56² = 3,136
And that’s it for this week’s post. We hope that you have enjoyed this post and that we have taught you how calculate the square of a number in a simpler way.
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