Squares 1 to 30

A square number is the product of a number multiplied by itself. It is commonly represented using exponent notation:

a²= a × a

Squares 1 to 30 Chart

Square 1 to 30 Table

The squares of numbers from 1 to 30, i.e, the square of the first 30 natural numbers given in the image discussed below,

Also check: Squares 1 to 50

Squares from 1 to 30 (Even Numbers)

Even numbers from 1 to 30 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, and 30. Learning the square of even numbers from 1 to 30 is very important. The following table contains the squares 1 to 30 for even numbers.

Squares from 1 to 30 (Odd Numbers)

Odd numbers from 1 to 30 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, and 29. Learning the squares of odd numbers from 1 to 30 is very important. The following table shows the values of squares from 1 to 30 for odd numbers.

Square of Negative Numbers

The square of a negative number is always positive because multiplying two negative numbers results in a positive product.
The square of a negative number results in a positive value, as shown in the table below:

Calculating Squares 1 to 30

The squares 1 to 30 can easily be calculated using the two methods as discussed below:

• Multiplication by Itself
• Using Algebraic Identities

Now, let's learn about these two methods in detail.

Method 1: Multiplication by Itself

Multiplying by itself means to find the square of the number we multiply the number with itself, i.e. the square of any number a is (a)² then it is calculated as (a)² = a × a.

Square of some numbers between 1 to 30 using the multiplication by itself method is,

• (4)² = 4 × 4 = 16
• (7)² = 7 × 7 = 49
• (12)² = 12 × 12 = 144
• (21)² = 21 × 21 = 441, etc

This method works best for smaller methods, but for finding the square of the larger numbers, we use other methods, i.e., using Algebraic Identities.

Method 2: Using Algebraic Identities

As the name suggests, using algebraic identities uses the basic identities of the square, i.e., it uses

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab

Now the given number "n" is broken according to these identities as,

n = (a + b) or n = (a - b) according to the number n, and then the square is found using the identities discussed above. This can be understood by the example discussed below.

For example: To find the square of 28, we can express 28 in two ways,

Solution:

(20 + 8)
To find the square of 28 we use the algebraic identity,
(a + b)² = a² + b² + 2ab
(20 + 8)² = 20² + 8² + 2(20)(8)
= 400 + 64 + 320
= 784

(30 - 2)
To find the square of 28 we use the algebraic identity,
(a - b)² = a² + b² - 2ab
(30 - 2)² = 30² + 2² - 2(30)(2)
= 900 + 4 - 120
= 784

This method is used to find the square of a large number very easily.

Tricks to Memorize Squares

Here are some helpful tricks to assist you in memorizing square roots:

• Squaring a number simply means multiplying it by itself.
• Start by memorizing the most common squares (from 1 to 9).
• For numbers ending in 5 (such as 5, 15, 25), use the equation: n(n + 1), followed by 25.
  For example, for 25:
  2 × (2 + 1) = 6, followed by 25, giving you 625.
• Apply the algebraic tricks mentioned above to make it easier.
  For example: (29)²:
  (30 − 1)² = 30² × 30 × 1 + 1²
  29² = 900 − 60 + 1 = 841

Read More,

• Squares and Square Roots
• Square Root Formula
• Square root of 2
• Square Root of 3

Solved Examples on Squares of 1 to 30

Example 1: Find the area of the circular park whose radius is 21 m.

Solution:

Given,
Radius of Park = 21 m
Area of Circular Park(A) = πr²
A = π (21)²
Using the square of 21 from the square of 1 to 30 table
21² = 441
A = 22/7(441)
A = 1386 m²

Thus, the area of the circular park is 1386 m²

Example 2: Find how much glass is required to cover the square window of side 25 cm.

Solution:

Given,
Side of Square Window(s) = 25 cm
Area of Square Window(A) = (s)²
A = (25)²
Using the square of 25 from the square of 1 to 30 table
25² = 625
A = 625 cm²

Thus, the glass required to cover the square window is 625 cm²

Example 3: Simplify 11² - 5² + 21²

Solution:

Using Square of 1 to 30 table we get,

• 11² = 121
• 5² = 25
• 21² = 441

Simplifying, 11² - 5² + 21²
= 121 - 25 + 441
= 562 - 25
= 537

Example 4: Simplify 16² + 15² - 19²

Solution:

Using Square of 1 to 30 table we get,

• 16² = 256
• 15² = 225
• 19² = 361

Simplifying, 16² + 15² - 19²
= 256 + 225 - 361
= 481 - 361
= 120

Solved Question On Squares of 1 to 30

Question 1: Find the area of a square window whose side length is 17 inches.

Solution:

Area of the Square window (A) = Side²
Using the squaretable 1 to 30, we get,
Area = 17² = 289
Therefore, the area of the window is 289 inches

Question 2: What is the square of 26?

Solution:

Using the value from square table 1 to 30 chart,
we can get the square of 26 which is 26² = 676

Question 3: Two square wooden planks have sides 5 m and 12 m,, respectively. Find the combined area of both wooden planks.

Solution:

Area of wooden plank = (side)²
Let us use the chart of square upto 30 to solve this question

Area of 1st wooden plank = 5² = 25
Area of 2nd wooden plank = 10² = 100

Therefore, the combined area of wooden plank is 100 + 25 = 125 m²

Question 4: If a circular tabletop has a radius of 25 inches, what is the area of the tabletop in sq. inches?

Solution:

Area of circular tabletop = πr² = π (25)²
Let us use the value from squares of 1 to 30 chart and we get
(25)² = 625
Area = 625π

Therefore, the area of tabletop = 1963.50 inches²

Unsolved Question On Squares 1 to 30

Question 1: Find the area of a square garden whose side length is 14 meters.

Question 2: What is the square of 19?

Question 3: Two square carpets have sides 8 m and 15 m, respectively. Find the combined area of both carpets.

Question 4: A circular garden has a radius of 12 feet, what is the area of the garden in square feet?

Answer Sheet

1) 196 meters²
2) 361
3) 289 merters²
4) 452.39 square feet