Square 1 to 30

Square 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 square 1 to 30 in the exponential form is expressed as (x)².

Square 1 to 30:

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

1.	Square 1 to 30
2.	Square 1 to 30 PDF
3.	How to Calculate Square 1 to 30?
4.	FAQs

Squares 1 to 30 Chart

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.

Square 1 to 30 - Even Numbers

The table below 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

Square 1 to 30 - Odd Numbers

The table below 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 from 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.

Solved Examples on Square 1 to 30

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

Solution:

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

Using values from square 1 to 30 chart;

i.e. A = 256π

Therefore, the area of the tabletop = 804.25 inches².
Example 2: Find the area of a square window whose side length is 25 inches

Solution:

Area of square window (A) = Side²

i.e. A = 25² = 625

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

Solution:

Area of wooden plank = (side)²

⇒ 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: Find the sum of the first 30 odd numbers.

Solution:

The sum of first n odd numbers is given as n²

⇒ Sum of first 30 odd numbers (n) = 30²

Using values from square 1 to 30 chart, the sum of first 30 odd numbers = 900

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FAQs on Square 1 to 30

What is the Value of Square 1 to 30?

The value of square 1 to 30 is the list of numbers obtained by multiplying an integer(1 - 30) by itself. It will always be a positive number.

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:

Finding Square 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 squares of numbers 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, and 30 will be even.

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

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 Squares 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 numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 will 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 1² (1), 2² (4), 3² (9), 4² (64), 5² (25), 6² (36), 7² (49), 8² (64), 9² (36), and 10² (100).