# What is the digit at units place of the cube root of 2197?

A system was introduced to define the numbers present from negative infinity to positive infinity. The system is known as the Number system. Number system is easily represented on a number line and Integers, whole numbers, natural numbers can be all defined on a number line. The number line contains positive numbers, negative numbers, and zero. Number system is defined in two ways, the Indian and International way of writing numbers, in Indian style, the commas are added from right to left. The numbers are defined with the unit place, tens place, hundreds, and so on.

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**Question: What comes on the unit place of the number 12,689?**

**Answer:**

9 number comes at the unit place of the number 12,689.

### Cube and Cube root of a Number

The cube of a number is defined as the number multiplied by itself 3 times. Cube root is the opposite of cube, that is, the cube of a cube root value gives the original number. For example, the cube of 5 is 5× 5× 5= 125, and the cube root of the 125 will give the original number 5.

If x is a number and the cube root of x is required, **cube root of x is written as** ⇢ or (x)^{1/3}

**Question: Find the cube of 7, will the cube root of the result give 7 again?**

**Solution: **

The cube of 7 is,

7 × 7 × 7= 49 × 7

= 343

The cube root of 343 will give 7 back again.

Note:Cube and cube root are co-related and are opposite of each other.

### Digit at the Unit place of Cube root of 2197

In order to find the digit at the unit’s place of the cube root of 2197, the cube root of 2197 is required, however, there are simpler methods that can be used to find the unit’s place value of the cube root of 2197. Prime factorization and Estimation methods are the methods that can be used. In this case, the best-suited method is the Estimation method.

**Using the Estimation method to find the unit place value **

- It is important to have the knowledge of the basic cubes and cube roots, that is, the cube and cube roots from 1 to 10,

Numbers | Cubes |

1 | 1 |

2 | 8 |

3 | 27 |

4 | 64 |

5 | 125 |

6 | 216 |

7 | 343 |

8 | 512 |

9 | 729 |

10 | 1000 |

- Now, notice the unit’s place of the number 2197, that unit’s place value is 7, look into the above table, and figure out the number that provides a cube value with 7 as unit place digit.
- The number is 3, as the cube of 3 is 27 and the unit’s place value of 27 is 7.
- Hence, it can be concluded that the unit’s place value of the cube root of 2197 is
**3**.