The **square root of 12 **is represented in the radical form asÂ **âˆš**12, which is equal to 2âˆš3.Â Since 2âˆš3 cannot be further simplified, hence such roots are called **surds**. Apart from representing the value of root 12 in radical form, it can also be written in the decimal form, such as **âˆš12 = 3.464,** up to three places of decimals.Â Now the question comes how to find the value of root 12? 12 is not a perfect square like numbers such as 2, 3, 5, 6, 24, 13, 125, etc. Hence, its simplification is a little typical. But numbers like 4, 16, 25, 81, 121, etc. are the perfect squares and its easy to estimate the square roots.Â We get square of a number when we multiply the number by itself. Let us first take the examples of a few squares.

For example,

11^{2 }Â = 11 Ã— 11 = 121

9^{2} =^{Â }9 Ã— 9 = 81

5^{2 }= 5 Ã— 5 = 25

Therefore, in the above examples, 11, 9 and 5 are the square numbers. But if we have to find out that a number is a perfect square or not, we need to check the unit place of the number.

- If at the unit place, the number ends with 2, 3, 7 and 8, then the number is not a perfect square.
- A perfect square number ends with 1, 4, 5, 6 and 9.

The symbol represents the square root, â€˜**âˆšâ€™**. This symbol â€˜**âˆšâ€™** is called a **radical symbol or radix**. The number underneath the radical symbol or radix is called as **radicand**.

## How to Find Value of Root 12?

The root of 12 is represented in the form of âˆš12. Number 12 is an even number and not a prime number. Prime numbers have only two factors, 1 and the number itself, such as 1, 3, 5, etc. As we know, 12 have six factors, 1, 2, 3, 4, 6 and 12 itself, such as,

1 Ã— 12 = 12

2 Ã— 6 = 12

3 Ã— 4 = 12

4 Ã— 3 = 12

6 Ã— 2 = 12

12 Ã— 1 = 12

But the question comes, how can we find out the square root value of 12? First, let us write the factors of 12 as given below.

12 = 2 Ã— 2 Ã— 3

You can see, in the above expression, there is only one square number available on the right-hand side. Therefore, the value of the root of 12 can be written as;

Taking the square term out of the root we get,

âˆš12 = 2 âˆš3

This is the radical form of âˆš12. We can also write it in decimal form, by putting the value of âˆš3 which is approximately 1.73. Hence,

âˆš12 = 2 Ã— 1.73

**âˆš12 = Â±3.46 approximately.**

Like 12, there are also many numbers which are not perfect squares. For example, 18, 20, 27, etc. are not perfect squares, as they give the value in radical form or decimal form.

**Also, find:**

### Table of Squares and Square Root From 1 to 15

To simplify questions based on the square root of numbers from 1 to 15, we are providing here the table of squares and square root, so that it is easy to identify which numbers are perfect squares and which are not.

Number | Squares | Square Root (Upto 3 places of decimal) |

1 | 1^{2} = 1 |
âˆš1 = 1 |

2 | 2^{2} = 4 |
âˆš2 = 1.414 |

3 | 3^{2} = 9 |
âˆš3 = 1.732 |

4 | 4^{2} = 16 |
âˆš4 = 2.000 |

5 | 5^{2} = 25 |
âˆš5 = 2.236 |

6 | 6^{2} = 36 |
âˆš6 = 2.449 |

7 | 7^{2} = 49 |
âˆš7 = 2.646 |

8Â | 8^{2} = 64 |
âˆš8 = 2.828 |

9Â | 9^{2} = 81 |
âˆš9 = 3.000 |

10 | 10^{2} = 100 |
âˆš10 = 3.162` |

11 | 11^{2} = 121 |
âˆš11 = 3.317 |

12 | 12^{2} = 144 |
âˆš12 = 3.464 |

13 | 13^{2} = 169 |
âˆš13 = 3.606 |

14 | 14^{2} = 196 |
âˆš14 = 3.742 |

15 | 15^{2} = 225 |
âˆš15 = 3.873 |

Download BYJUâ€™S – The Learning App and learn to find the squares and roots of numbers with the help of interactive videos.