Shortcut to Find Square of a Number

Today I will discuss a very simple method of finding square of numbers between 26 to 74 mentally. In the subsequent post we will cover higher numbers. So keep watching this space to learn squaring any number within your mind

Square (also called perfect square) is an integer that is the square of an integer; in other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 3 × 3.

How to find the square of any number?

To apply this method you should know squares of 1 to 25 by heart. You can refer to this table to learn the same.

Number Square Number’ Square’
1 1 13 169
2 4 14 196
3 9 15 225
4 16 16 256
5 25 17 289
6 36 18 324
7 49 19 361
8 64 20 400
9 81 21 441
10 100 22 484
11 121 23 529
12 144 24 576
* * 25 625

For finding square of any number between 26 to 75

 

Step 1. Find the difference between 50 and the number you want to square.

Scenario 1: If the number to be squared is greater than 50

Step 2. Add that many 100s to 2500 (which is the square of 50)

Step 3. Then add the square of the difference to the result of step 1

Scenario -2: If the number is less than 50

Step 2. Subtract that many 100s to 2500.

Step 3. Then add the square of the difference to the result of step 1

Example

Find out the Square of 67.

Step 1. Difference of 67 and 50 = 67-50 = 17
Step 2. This number is greater than 50. So add 1700 to 2500 = 4200
Step 3. Add square of 17 to step 2.

Answer = 4200+ 289 = 4489

Alternative method of calculating the square of a number:

Since, 67-50 = 17

67^2

We will be getting answer in 2 parts; see below – right hand side gives you tens and units digit. Left hand side gives you the remaining digits.

= 25 + 17 | (17)^2 ( | denotes separation )

= 42 | 289 (17^2 is 289. The 2 shown in subtext will be carried over and added to left hand side)

= 4489

Check out another shortcut and quick method of finding square of any 2 digit number

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