Square Root 1 to 30: In the study of Mathematics, the square root of a number is defined as a number that if multiplied by itself then results in the original number. For example, the square root of 16 is 4. If 4 is multiplied by 4, then we have 9. Square roots of any number generally have both values on negative and positive sides. The positive values of square roots of numbers from 1 to 30 cover the range from 1 to 5.477. In this article, you will get to know more about the values of square root 1 to 30, the list and chart of square roots of numbers from 1 to 30, methods to find out the square roots, and solved examples.
What is the Square Root 1 to 30?
The square root of a number from 1 to 30 is generally expressed as √x. But in the case of the exponential form, the square root is expressed by x^(½), where x = 1 to 30 numbers. For example, √49 = 7.
Here, x = 49
Hence, the value of the square root of 49 is 7.
Square Root 1 to 30 Chart
The square root 1 to 30 chart helps you to quickly learn the values of the square roots of numbers from 1 to 30. It also simplifies the time-consuming long equations. The value of square roots of numbers from 1 to 30 up to 3 decimal places is 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 |
For faster maths calculations, students are suggested to memorize the square roots 1 to 30 values thoroughly.
Square Root 1 to 30 for Perfect Square Number
In square roots 1 to 30, the numbers 1, 4, 9, 16, and 25 are considered the perfect squares, and the remaining numbers are called the non-perfect squares. The following given table describes the values of square roots from 1 to 30 for perfect square numbers.
Square Root 1 to 30 for Perfect Square Number | |
√1 = 1 | √4 = 2 |
√9 = 3 | √16 = 4 |
√25 = 5 |
Square Root 1 to 30 for Non-Perfect Square Number
Excluding the numbers 1, 4, 9, 16, and 25, all numbers from 1 to 30 are considered non-perfect square numbers (their square root will be in irrational form). The following given table describes the values of square roots from 1 to 30 for non-perfect square numbers.
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?
Mainly there are two methods given below for calculating the values of square roots of numbers from 1 to 30.
Method 1- Prime Factorization
For perfect square numbers like 1, 4, 9, 16, and 25, the prime factorization method can be used to find square roots easily.
Question: Find out the value of √81 by using the prime factorization method.
Solution: The prime factorization of 81 is 9 × 9
Here, the pairing prime factors are 9
Thus, the value of √81 is 9.
Method 2- Long Division Method
For non-perfect square numbers like 2, 3, 5, 6, 7, 8, 10, etc., the long division method can be used.
Question: Find out the value of √15 by using the long division method.
Solution:

Square Root 1 to 30 Solved Questions
Question 1: Find out the value of the square root of 324.
Solution: By using the prime factorization method,
We get, 324 = 2 x 2 x 3 x 3 x 3 x 3
√324 = √(2 x 2 x 3 x 3 x 3 x 3)
√324 = 2 x 3 x 3 = 18
Question 2: Solve out for the square root of 8.
Solution: By using the prime factorization method,
We get, 8 = 2 x 2 x 2
√8 = √(2 x 2 x 2) = 2√2
Question 3: A square plastic board has an area of 64 sq. inches. Solve out the length of the side of that plastic board.
Solution: Suppose x is the length of the side of the plastic board
Area of the square plastic board = 64 inches^2 = a^2
a^2 = 64
a = √64 = 8 inches
Hence the length of the side of the plastic board is 8 inches.
Question 4: When a circular carpet has an area of 36π sq. inches. Calculate the radius of that carpet.
Solution: Given that the area of circular carpet = 36π in^2 = πr^2
After canceling π on both sides, we get 36 = r^2
Hence, radius = √36 = 6 inches
Question 5: Calculate the value of 3√7 + 2√10
Solution: Putting the value of √7 = 2.646 and √10 = 3.162, we get
3√7 + 2√10 = 3 × (2.646) + 2 × (3.162)
Hence, 3√7 + 2√10 = 7.938 + 6.324 = 14.262