# Value of Root 3

The **value of root 3** is a positive real number when it is multiplied by itself; it gives the number 3. It is not a natural number but a fraction. The square root of 3 is denoted by **√3**. The square root basically, gives a value which, when multiplied by itself gives the original number. Hence, it is the root of the original number.

To find the square root of any real number, without using a calculator, we need to check first if the number under the root is a perfect square or not. If a number is a perfect square, then we can easily find its square root using prime factorisation method. For example, the square root of 4 is ±2, since 2^{2} = 4. But, here 3 is an imperfect square or a non-perfect square. Hence, we cannot use the factorisation method. Instead, we will be using the long division method to find the value of the square root of 3. The actual value of √3 is given below.

Value of root 3, √3 =1.732 |

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## Root 3 Value in Maths

In Maths, we used to calculate the square root values of many numbers. Some numbers are perfect squares, but some are non-perfect. We can calculate the root of perfect squares easily by just the factorisation method but to find the root of non-perfect squares, we have to use the long division method. The number 3 is also a non-perfect square. Hence, the value of the square root of 3 can be calculated using the long division method.

## How to find the value root of 3?

As it is mentioned above, the easiest way to finding the root value of imperfect square numbers is by using long division.

Since 3 is a non-perfect square number, we will find the value of root 3 using long division method as follows

Therefore, the value of root 3 is

**√3 = 1.73205080757**

While solving mathematical problems, we can use the round off value of root 3 up to three decimal place.

**√3 = 1.732**

### Table of Square Root

**Below is the table to find the square root values from number 1 to 25.**

Number |
Square Root (√) |

1 | 1.000 |

2 | 1.414 |

3 | 1.732 |

4 | 2.000 |

5 | 2.236 |

6 | 2.449 |

7 | 2.646 |

8 | 2.828 |

9 | 3.000 |

10 | 3.162 |

11 | 3.317 |

12 | 3.464 |

13 | 3.606 |

14 | 3.742 |

15 | 3.873 |

16 | 4.000 |

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 | 5.000 |

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## Frequently Asked Questions – FAQs

### What is the value of root 3?

### What is the approximate value of √3?

√3 = 1.732

### How can we find the value of √3?

### What is the value of root 2 and root 5?

√2 = 1.414

√5 = 2.236

### What is the value of 3√4?

3√4 = 3 x 2 = 6.