Shortcut to Find Square of a Number
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 |
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
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 |
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
