# Square of a Number – Definition, Examples | How to Find the Square of a Number?

The square of a number means multiplying a number by itself. The perfect square numbers are the squares of a whole number. Get the important properties of the square numbers and tricks to calculate the square of a number easily in the following sections. We have also provided example questions and answers that help to understand the concept.

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## What is the Square of a Number?

In mathematics, the square of a number is defined as the product of multiply the number by itself. The word square means raising a number to power 2 and denoted by the superscript 2. We can find a number square by using the long multiplication method.
Example:
27² = 27 x 27

Therefore, 27² = 729

### How to Find the Square of a Number?

Follow the simple guidelines and instructions to calculate the square of a number and they are along the lines:

• Write the numbers in two different columns.
• Multiply the unit digit of the below number by the first number.
• Write the product below
• Again multiply the ten’s digit of the below number by the first number.
• Write the product in the fourth row.
• Add the products of the third and fourth row to get the number square.

Math Trick For Finding Square of a Two-Digit Number

• Add the unit digit of the number to the original number.
• Multiply the sum by the ten’s digit of the original number.
• Find the square of the last digit of the original number.
• Append the square number (step 3) to the product calculated above (step 2).

### Square Numbers Up to 15

Below mentioned is the list of squares of the numbers from 1 to 15.

### Properties of Square Numbers

• A number ending with 2, 3, 7, or 8 is never a perfect square of a number.
• The square of even numbers is always an even number and the square of an odd number is also an odd number.
• The numbers ending with 2, 3, 7 or 8 is not a square number.
• If a number has 1 or 9 in the unit’s place, then its square ends with 1.
• If a number has 4 or 6 in the unit’s place, then its square ends with 6.
• A perfect square number always leaves a remainder 0 or 1 when divided by 4.

### Square of a Number Examples

Example 1:
Find the square of 53.
Solution:
The given number is 53
53 + 3 = 56
56 x 5 = 280
3² = 9
So, 53 x 53 = 2809
Therefore, the square of 53 is 2809.

Example 2:
The square of a number is 441. What is the original number?
Solution:
Given that,
The Square of a number is 441
Write the factors of 441
441 = 3 x 3 x 7 x 7
= (3 x 7)² = 28²
Therefore, the original number is 28.

Example 3:
Solve the square of the following number using the math trick and verify it.
(i) 76
(ii) 42
(iii) 29
Solution:
(i) Given number is 76
Find the square of 76 using the math trick.
Add the unit digit of the number to the original number.
6 + 76 = 82
Multiply the sum by the ten’s digit of the original number.
82 x 7 = 574
Find the square of the last digit of the original number.
6² = 36
Append the obtained numbers in the above two steps.
5740 + 36 = 5776

Therefore, 76² = 5776
(ii) Given number is 42
Find the square of 42 using the math trick.
Add the unit digit of the number to the original number.
2 + 42 = 44
Multiply the sum by the ten’s digit of the original number.
4 x 44 = 176
Find the square of the last digit of the original number.
2² = 4
Append the obtained numbers in the above two steps.
42² = 1764

Therefore, square of 42 is 1764
(iii) Given number is 29
Find the square of 29 using the math trick.
Add the unit digit of the number to the original number.
9 + 29 = 38
Multiply the sum by the ten’s digit of the original number.
2 x 38 = 76
Find the square of the last digit of the original number.
9² = 81
Append the obtained numbers in the above two steps.
760 + 81 = 841

Therefore, the square of 29 is 841.

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