Square Root 1 to 30: List, Chart, and Calculation Methods

In mathematics, the square root of a number is a value that, when multiplied by itself, produces the original number. Square roots can yield both positive and negative values. Denoted by the radical symbol (√), this operation is essential for calculating geometric dimensions or solving quadratic equations. The square root of a number (x) is written as √x in radical form or x½ in exponential form. For instance, the square root of 16 is 4, because 4 multiplied by 4 equals 16.

The positive square roots of integers from 1 to 30 range from 1 to approximately 5.477. This guide provides a detailed list and chart of square roots for numbers 1 through 30, along with easy-to-follow calculation methods and practical examples.

What is the Square Root 1 to 30?

Square roots for numbers 1 to 30 are typically represented as √x or, using exponents, as x^(½), where x ranges from 1 to 30. For example, √49 = 7.

In this case, x = 49.

Therefore, the square root of 49 is 7.

Square Root 1 to 30 Chart

The square root 1 to 30 chart is a valuable tool for simplifying complex equations and performing quick mental math. The values of the square roots from 1 to 30, rounded to three decimal places, are listed below.

Square Root from 1 to 30 Chart
√1 = 1	√2 = 1.414
√3 = 1.732	√4 = 2
√5 = 2.236	√6 = 2.449
√7 = 2.646	√8 = 2.828
√9 = 3	√10 = 3.162
√11 = 3.317	√12 = 3.464
√13 = 3.606	√14 = 3.742
√15 = 3.873	√16 = 4
√17 = 4.123	√18 = 4.243
√19 = 4.359	√20 = 4.472
√21 = 4.583	√22 = 4.690
√23 = 4.796	√24 = 4.899
√25 = 5	√26 = 5.099
√27 = 5.196	√28 = 5.292
√29 = 5.385	√30 = 5.477

To improve efficiency in mathematical calculations, students are encouraged to memorize these square root values.

Square Root 1 to 30 for Perfect Square Number

Within the range of 1 to 30, the numbers 1, 4, 9, 16, and 25 are identified as perfect squares, while the others are non-perfect squares. The number 1 is unique as it is the only integer whose square root is equal to itself. The following table highlights the perfect square roots in this range.

Square Root 1 to 30 for Perfect Squares

• √1 = 1 
• √4 = 2
• √9 = 3 
• √16 = 4
• √25 = 5

Square Root 1 to 30 for Non-Perfect Square Number

Excluding 1, 4, 9, 16, and 25, all other numbers from 1 to 30 are non-perfect squares, resulting in irrational numbers. The table below outlines the square root values for these non-perfect squares.

Square Root 1 to 30 for Non-Perfect Square Number
√2 = 1.414	√3 = 1.732
√5 = 2.236	√6 = 2.449
√7 = 2.646	√8 = 2.828
√10 = 3.162	√11 = 3.317
√12 = 3.464	√13 = 3.606
√14 = 3.742	√15 = 3.873
√17 = 4.123	√18 = 4.243
√19 = 4.359	√20 = 4.472
√21 = 4.583	√22 = 4.690
√23 = 4.796	√24 = 4.899
√26 = 5.099	√27 = 5.196
√28 = 5.292	√29 = 5.385
√30 = 5.477

How to Calculate Square Root 1 to 30?

There are two primary methods used to calculate the square roots of numbers between 1 and 30.

Method 1- Prime Factorization 

For perfect square numbers like 1, 4, 9, 16, and 25, the prime factorization method is the most efficient way to find the square root.

Question: Calculate √81 using the prime factorization method.

Solution: The prime factors of 81 are 9 × 9.

Grouping the prime factors, we have 9.

Thus, the value of √81 is 9.

Method 2- Long Division Method 

For non-perfect square numbers such as 2, 3, 5, 6, 7, 8, 10, and others, the long division method is typically applied.

Question: Calculate the value of √15 using the long division method.

Solution:

Square Root 1 to 30 Solved Questions

Question 1: Find the square root of 324.

Solution: Applying the prime factorization method:

324 = 2 × 2 × 3 × 3 × 3 × 3

√324 = √(2 × 2 × 3 × 3 × 3 × 3)

√324 = 2 × 3 × 3 = 18

Question 2: Solve for the square root of 8.

Solution: Using prime factorization:

8 = 2 × 2 × 2

√8 = √(2 × 2 × 2) = 2√2

Question 3: A square plastic board has an area of 64 sq. inches. Determine the length of its side.

Solution: Let x represent the length of the side of the board.

Area = 64 sq. inches = a²

a² = 64

a = √64 = 8 inches

Therefore, the side length of the plastic board is 8 inches.

Question 4: A circular carpet has an area of 36π sq. inches. Calculate its radius.

Solution: Area = 36π sq. inches = πr²

By dividing both sides by π, we get 36 = r²

Thus, the radius = √36 = 6 inches.

Question 5: Calculate the value of 3√7 + 2√10.

Solution: Using √7 ≈ 2.646 and √10 ≈ 3.162:

3√7 + 2√10 = 3 × (2.646) + 2 × (3.162)

Therefore, 7.938 + 6.324 = 14.262.