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Dec12

Square Number: Some Tricks and Examples

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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. 

square 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:

  1. We remove the units ones place digit from the number, that is to say, we remove the 5.
  2. We multiply the number that remains by the number that comes after this number when counting.
  3. We add the number 25 on to the end of the result of the previous multiplication.
  4. We already have the result of taking the square of that number.
Let’s look at an example: 25²
  1. We take the number 25 and remove the 5. So only the 2 remains.
  2. We multiply the 2 by the number that follows it when counting (so 3) following number:

2 x 3 = 6

  1. After the 6 we add the number 25:

625

  1. We have already arrived at the result of the operation:

25² = 625

 

Another example: 405²
  1. We take the number 405 and remove the 5. We are left with 40.
  2. We multiply 40 by the number that follows it when counting (so 41) following number:

40 x 41 = 1,640

  1. We add 25 on to the end of the number:

164,025

  1. We have already arrived at the correct result:

405²= 164,025

 

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:

  1. We subtract 25 from the number. This number will be the first two digits of the final result.
  2. We find the difference between 50 and the number.  
  3. We square that difference and the result will be the last two digits of the final result.
 Let’s look at an example: 47²
  1. We subtract 25 from the number. These will be the first two digits of the number.

47 – 25 = 22

 

  1. The difference between 50 and 47 is:

50 – 47 = 3

  1. We square the number 3:

 = 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
  1. We subtract 25 from the number:

56 – 25 = 31

  1. We take the difference between the number and 50:

56 – 50 = 6

  1. We square the previous number:

 = 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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