Square Root 1 to 30

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.

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 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.

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