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. The square root of any number can be** both negative and positive values**. It is denoted by the radical symbol (√) and is used to find the side length of a square with a given area or to solve quadratic equations. The square root of any number (x) in radical form is expressed as √x and in the exponential form it is expressed as (x)½ For example, the square root of 16 is 4. If 4 is multiplied by 4, then we have 9.

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 roots 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 square root of 1 is the only whole number whose square root is equal to itself. 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 inches²= a²

a² = 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 in² = πr²

After canceling π on both sides, we get 36 = r²

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