# Cube Root of 3

The value of the **cube root of 3 **is equal to 1.44224957031. Cube root of 3 in radical form is represented as ^{3}√3 and in exponential form as 3^{1/3}. Since 3 is not a perfect cube, therefore it is a little difficult to find its cube root. But, for perfect cubes like 8, 27, etc., the cube root of such numbers are whole numbers, because, 2^{3} = 2×2×2 = 8 and 3^{3} = 3×3×3 = 27. Hence, cube root of 8 is 2 and of 27 is 3.

Cube root of any number n is a number x, such as x^{3} = n. Hence, to find the cube root of 3 we have to determine a number, which when multiplied three times, gives the number 3, such as x^{3} = 3 or x = ^{3}√3. Therefore, we need to find here the value of x. In this article, we will learn to find cube root by the approximation method.

**Cube Root Symbol:** The symbol of cube root is ‘^{3}√’

## What is Cube Root of 3?

The cube root of 3 is a value that results in the original number when multiplied by itself, three times. Since 3 is a prime number, thus, it has only two factors, 1 and 3. Hence, 3 cannot be factorised into a product of three whole numbers. So, the cube root of 3 is a fraction or decimal value. Also, the cube root of 3 is a rational number, since it cannot be expressed in the form of P/Q, where Q ≠ 0. It is represented by ^{3}√3, in radical form.

^{3}√3 = 1.4422 (up to four places of the decimal)

## How to find Cube root of 3?

Before we learn to find the cube root of number 3, we have to first learn the cubes of these numbers.

Number (x) |
Cube of Number (x^{3}) |

1 | 1×1×1 = 1 |

2 | 2×2×2 = 8 |

3 | 3×3×3 = 27 |

4 | 4×4×4 = 64 |

5 | 5×5×5 = 125 |

6 | 6×6×6 = 216 |

7 | 7×7×7 = 343 |

8 | 8×8×8 = 512 |

9 | 9×9×9 = 729 |

10 | 10×10×10 = 1000 |

### Steps to find Cube Root Easily

Now, let us figure out the value of ^{3}√3, step by step.

**Step 1:** Let us assume the cube root of 3 is equal to x.

Then, x = ^{3}√3

**Step 2:** As we know,

1^{3} = 1 and 2^{3} = 8

Hence, x lies between 1 and 8. But, it lies closer to number 1 than 8, if we see in a number line. Hence, we can assume a value, say 1.4, which could be approx to the cube root of 3.

**Step 3:** Now to determine the value of ^{3}√3, we need to divide 3 by the estimated value.

Divide 3 by 1.4.

3/1.4 = 2.1428

**Step 4:** Again, divide this value by 1.4.

2.1428/1.4 = 1.53

**Step 5:** Now, take the average of 1.4, 1.4 and 1.53 to get a value of ^{3}√3.

(1.4+1.4+1.53)/3 = 1.44

The actual value of ^{3}√3 is 1.442249.

Hence, 1.44 is approximately equal to 1.442249.

**Cube Root Lists **

Below is the table for the cube root of numbers from 1 to 15.

Number |
Cube root ∛a |

1 | 1.000 |

2 | 1.260 |

3 | 1.442 |

4 | 1.587 |

5 | 1.710 |

6 | 1.817 |

7 | 1.913 |

8 | 2.000 |

9 | 2.080 |

10 | 2.154 |

11 | 2.224 |

12 | 2.289 |

13 | 2.351 |

14 | 2.410 |

15 | 2.466 |

## Solved Examples

**Q.1: The volume of a cube is 24 cu.cm. What is the length of its edges?**

Solution: Given,

volume of cube = 24 cu.cm

By the formula, we know,

volume of cube = a^{3}, where a is the edge-length

24 = a^{3}

a = ^{3}√24 = ^{3}√(2 x 2 x 2 x 3) = 2^{3}√3 = 2 x 1.442 = 2.884 cm

Hence, the length of edges of the cube is 2.884 cm.

**Q.2: What is the value of ^{3}√27 + ^{3}√3 + ^{3}√125? (Answer in radical form)**

Solution: ^{3}√27 + ^{3}√3 + ^{3}√125

= ^{3}√(3 x 3 x 3) + ^{3}√3 + ^{3}√(5 x 5 x 5)

= 3 + ^{3}√3 + 5

= 8 + ^{3}√3

## Frequently Asked Questions – FAQs

### What is the value of cube root of 3?

### What is the value of cube root of 3 in radical form?

^{3}√3.

### Is 3 a perfect cube?

### What is the cube of cube root of 3?

Students can learn these values and solve questions based on them easily.