Squares Upto 50

The square of a number is obtained by multiplying the number by itself. If Y is a number, then the square of it will be Y × Y = Y². For example, the square of 3 is 3² = 3 × 3 = 9. Squares up to 50 is a list of squares of all the numbers from 1 to 50.

Let’s understand the square shape in geometry. The square shape has all its sides equal in length. Also, we know that the area of a square is equal to the square of its side i.e. Area of Square = Side × Side = Side².

Similarly, the square numbers are the product of a number by itself. And the square of a number is expressed as Y × Y = Y². Read the article below to know 1 to 50 squares.

What is a Perfect Square?

A perfect square is an integer that can be represented as the product of two equal integers. For example, 25 is a perfect square because it equals 5 × 5 = 25. If Y is an integer then, Y² is a perfect square. Because of this definition, the outcome of perfect squares is always in non-negative form.

Square Table from 1 to 50

Below is the list of squares up to 50 in a tabular form:

Squares From 1 to 50

How to Calculate Squares of Even Numbers?

There are 25 even numbers from 1 to 50. As we know, even numbers are represented in the form of 2n, where n = 0, 1, 2, 3, 4, 5…..

Therefore the square of even numbers can be represented as (2n)² = 4n²

• If n = 1 , then the number will be 2(1) = 2 and the square will be 4n² = 4(1)² = 4

• If n = 2 , then the number will be 2(2) = 4 and the square will be 4n² = 4(2)² = 16

Table of Square of Even Numbers from 1 to 50

How to Calculate Squares of Odd Numbers?

Similar to even numbers there are 25 odd numbers from 1 to 50. As we know, odd numbers are represented in the form of 2n + 1, where n = 0, 1, 2, 3, 4, 5…..

Therefore the square of odd numbers can be represented as (2n + 1)² = 4n² + 4n + 1 = 4n ( n + 1) + 1

• If n = 0 , then the number will be 2(0) + 1 = 1 and the square will be 4n ( n + 1) + 1 = 4(0)(0 + 1) + 1 = 0 + 1 = 1

• If n = 1 , then the number will be 2(1) + 1 = 3 and the square will be 4n ( n + 1) + 1 = 4(1)(1 + 1) + 1 = 4(2) + 1 = 9

• If n = 2 , then the number will be 2(2) + 1 = 5 and the square will be 4n ( n + 1) + 1 = 4.2(2 + 1) + 1 = 8(3) + 1 = 25

Table of Square of Odd Numbers from 1 to 50

How to Calculate the Square of a Number?

To calculate the squares of number, we can use any of the following methods:

• Method 1: Multiply the number by itself.

• Method 2: Find the square of a number using the algebraic identity given below.

• (a + b)² = a² + b² + 2ab

• (a - b)² = a² + b² - 2ab

Example: Find the square of 45 using the algebraic identity.

Solution: We can express 45 in two ways as : ( 40 + 5) Or (50 - 5)

Let’s take ( 40 + 5) and using the identity (a + b)² = a² + b² + 2ab, we get:

(40 + 5)² = 40² + 5² + 2 40 5

(45)² = 1600 + 25 + 400

(45)² = 2025

Or

Let’s take (50 - 5) and using the identity (a - b)² = a² + b² - 2ab, we get:

(50 - 5)² = 50² + 5² - 2 50 5

(45)² = 2500 + 25 - 500

(45)² = 2025

Did You Know

For any number we can use both algebraic identities to find the square of the number. For example, for the square of 16, we can write 16 as (10+6) or (20-4) and use both identities (a + b)² = a² + b² + 2ab and (a - b)² = a² + b² - 2ab.

Solved Example

1. Find the area of the square window whose side length is 16 inches.

Ans: Area of a square window (A) = (Side)²

i.e. A = (16 inches)² = 256 inches²

Therefore, the area of a square window is 256 inches².

2. Find the square of 32 using the algebraic identity: (a + b)² = a² + b² + 2ab

Ans: Using the identity, we get:

(30 + 2)² = 30² + 2² + 2 30 2

(32)² = 900 + 4 + 120

(32)² = 1024

Practice Questions

1. Find the square of 38 using the algebraic identity.

2. Find the square of 54 using the algebraic identity.

Conclusion

In this article we have studied squares of 1 to 50 numbers and perfect squares. We have separately studied the squares of even numbers and odd numbers. We have learned methods of calculating squares of a number.