Square 1 to 30

Squares 1 to 30 is the list of squares of all the numbers from 1 to 30. The value of squares from 1 to 30 ranges from 1 to 900. Memorizing these values will help students to simplify the time-consuming equations quickly. The squares from 1 to 30 in the exponential form are expressed as (x)².

Squares from 1 to 30

Exponent form: (x)²
Highest Value: 30² = 900
Lowest Value: 1² = 1

1.	What are Squares from 1 to 30?
2.	Square 1 to 30 PDF
3.	How to Calculate Square 1 to 30?
4.	FAQs on Square Numbers 1 to 30

Squares 1 to 30 Chart

The following chart shows the square table 1 to 30 which helps the students in memorizing it easily.

Squares from 1 to 30 - Squares of 1 to 30 - Square table 1 to 30

What are Squares from 1 to 30?

Learning squares 1 to 30 can help students to recognize all perfect squares from 1 to 900 and approximate a square root by interpolating between known squares. The values of squares 1 to 30 are listed in the table below.

List of All Squares from 1 to 30
1² = 1	2² = 4
3² = 9	4² = 16
5² = 25	6² = 36
7² = 49	8² = 64
9² = 81	10² = 100
11² = 121	12² = 144
13² = 169	14² = 196
15² = 225	16² = 256
17² = 289	18² = 324
19² = 361	20² = 400
21² = 441	22² = 484
23² = 529	24² = 576
25² = 625	26² = 676
27² = 729	28² = 784
29² = 841	30² = 900

☛ Square 1 to 30 PDF

The students are advised to memorize these squares 1 to 30 values thoroughly for faster math calculations. The link given above shows square 1 to 30 pdf which can be easily downloaded for reference.

Squares from 1 to 30 - Even Numbers

The even numbers from 1 to 30 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, and 30. The following table shows the values of squares 1 to 30 for even numbers.

2² = 4	18² = 324
4² = 16	20² = 400
6² = 36	22² = 484
8² = 64	24² = 576
10² = 100	26² = 676
12² = 144	28² = 784
14² = 196	30² = 900
16² = 256

1 to 30 Squares - Odd Numbers

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

1² = 1	17² = 289
3² = 9	19² = 361
5² = 25	21² = 441
7² = 49	23² = 529
9² = 81	25² = 625
11² = 121	27² = 729
13² = 169	29² = 841
15² = 225

How to Calculate the Values of Squares 1 to 30?

In order to calculate the squares of 1 to 30, we can use any one of the following methods:

Method 1: Multiplication by itself

In this method, the number is multiplied by itself and the resultant product gives us the square of that number. For example, the square of 4 = 4 × 4 = 16. Here, the resultant product '16' gives us the square of the number '4'. This method works well for smaller numbers.

Method 2: Using basic algebraic identities

In this method, a given number ‘n’ is first expressed in the form of either (a+b) or (a-b), where ‘a’ is a multiple of 10 and ‘b' is any number less than 10. Next, the basic algebraic identities formula is used to find the square of the given number. We can use any of the 2 basic algebraic identities formulas to calculate the square of a given number. (a + b)² = a² + b² + 2ab or (a - b)² = a² + b² - 2ab. The form where ‘b’ has a smaller value should be preferred.

For example, to find the square of 29, we can express 29 as

Option 1: (20 + 9)
Option 2: (30 - 1)

In the next step, we use the basic algebraic identity formula and get Option 1: [20² + 9² + (2 × 20 × 9)] or Option 2: [30² + 1² - (2 × 30 × 1)]. Solving the expressions further, we get Option 1: (400 + 81 + 360) = 841 or Option 2: (900 + 1 - 60) = 841.

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Solved Examples on Squares of 1 to 30

Example 1: If a circular tabletop has a radius of 16 inches, what is the area of the tabletop in sq. inches?

Solution:

Area of circular tabletop = πr² = π (16)²

Let us use the values from the squares of 1 to 30 chart and we get 16² = 256

Area = 256π

Therefore, the area of the tabletop = 804.57 inches².
Example 2: Find the area of a square window whose side length is 25 inches.

Solution:

Area of the square window (A) = Side²

Using the square table 1 to 30, we get, Area = 25² = 625

Therefore, the area of the window is 625 inches²
Example 3: Two square wooden planks have sides 10 m and 12 m respectively. Find the combined area of both the wooden planks?

Solution:

Area of wooden plank = (side)²

Let us use the chart of squares upto 30 to solve this question.

⇒ Area of 1st wooden plank = 10² = 100 m²

⇒ Area of 2nd wooden plank = 12² = 144 m²

Therefore, the combined area of wooden planks is 100 + 144 = 244 m²
Example 4: What is the square of 15?

Solution:

Using values from square table 1 to 30 chart, we can get the square of 15 which is 15² = 225

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FAQs on Square Numbers 1 to 30

What is the Value of Squares 1 to 30?

The value of squares upto 30 is the list of numbers obtained by multiplying an integer by itself. When we multiply a number by itself we will always get a positive number. For example, the square of 12 is 12² = 144.

What are the Methods to Calculate Squares from 1 to 30?

We can calculate the square of a number by using the a² + b² + 2ab formula. For example (19)² can be calculated by splitting 19 into 10 and 9. Other methods that can be used to calculate squares from 1 to 30 are as follows:

Finding Squares by Column Method
Finding Squares by Diagonal Method

If You Take Squares from 1 to 30, How Many of Them Will be Even Numbers?

The even numbers between 1 to 30 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, and 30. Since the squares of even numbers are always even, therefore, the value of the squares of all these numbers will also be even.

Using Squares 1 to 30 Chart, Find the Value of 31 plus 30 Square plus 21 Square.

Using the chart of squares up to 30, we know that the value of 30² is 900 and 21² is 441. So, 31 + 30² + 21² = 1372. Hence, the value of 31 plus 30 Square plus 21 Square is 1372.

How Many Numbers in the Square Table 1 to 30 are Odd?

The odd numbers between 1 to 30 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, and 29. Since the squares of odd numbers are always odd. Therefore, the value of squares of all these numbers will also be odd.

What is the Sum of all Perfect Squares from 1 to 30?

The sum of all perfect squares from 1 to 30 is 55, i.e., 1 + 4 + 9 + 16 + 25 = 55.

What Values of Squares from 1 to 30 are Between 1 to 100?

The values of squares 1 to 30 between 1 to 100 are as follows. 1 = 1², 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = (81), and 10² = (100).

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