# Square Root And Cube Root

**Square root and Cube roots** are the most important topics in Maths, especially for class 8 students. To find the *square root* of any number, we need to find a number which when multiplied twice by itself gives the original number. Similarly, to find the cube root of any number we need to find a number which when multiplied three times by itself gives the original number.

**Symbol:** The square root is denoted by the symbol ‘√’, whereas the cube root is denoted by ‘∛’.

**Examples:**

- √4 = √(2 × 2) = 2
- ∛27 = ∛(3 × 3 × 3) = 3

## Square Root and Cube Root Table

Memorizing the squares and the square roots of the first few numbers are almost elementary and it can help you to solve problems much faster rather than having to work on it. Following is the **square roots list** and **Cube root list** of the first 15 natural numbers.

Number |
Square root (√) |
Cube root (∛) |

1 | 1.000 | 1.000 |

2 | 1.414 | 1.260 |

3 | 1.732 | 1.442 |

4 | 2.000 | 1.587 |

5 | 2.236 | 1.710 |

6 | 2.449 | 1.817 |

7 | 2.646 | 1.913 |

8 | 2.828 | 2.000 |

9 | 3.000 | 2.080 |

10 | 3.162 | 2.154 |

11 | 3.317 | 2.224 |

12 | 3.464 | 2.289 |

13 | 3.606 | 2.351 |

14 | 3.742 | 2.410 |

15 | 3.873 | 2.466 |

## How to find Square Root and Cube Root

To find the square root of the number, we have to determine which number was squared to get the original number. For example, if we have to find the root of 16, then as we know, when we multiply 4 by 4, the result is 16. Hence, √16 = 4. Similarly, if we have to find the cube root of a number, say 64, then it is easy to determine that the cube of 4 gives 64. So the cube root of 64 is 4. But if the numbers are very large, then to find the roots, we have to use the prime factorisation method. Let us see some examples.

### Solved Examples

**Example 1: Find Square root of 256.**

Solution: Given: The number is 256.

Prime factorisation of 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = (2 × 2 × 2 × 2)^{2 }= 16^{2}

Taking roots on both the sides, we get;

√256 = 16.

Hence, 16 is the answer.

**Example 2: Find the cube root of 512.**

Solution:

Given: The number is 512.

Prime factorisation of 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = (2 × 2 × 2)^{3 }= 8^{3}

Taking the cube root on both the sides we get;

∛512 = 8

Hence, 8 is the answer.

**Related Links:**

Basically, square explains the area of a square, which is equal to ‘side x side’. But what if we have to find the side of the square. In such a case, we need to find the square root of the area of the square. In the same way, a cube explains the volume of the cube, which is equal to ‘side x side x side’. Now, if we have to find the length of the edges of the cube, then we need to determine the cube root of the volume of a cube.

If subtraction is the opposite of addition and division is the reverse method of multiplication, then square root and cube root are the inverse processes of finding squares and cubes of numbers. This concept has been widely explained in Class 8 syllabus. To find the square root as well cube root for a given number, we can use the prime factorisation method, which we will discuss here later.