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What is the cube of (−3)?

  • Last Updated : 03 Sep, 2021

In mathematics, when arithmetic calculations are performed or measuring any objects such as the length of a park, area of a rounded table, etc., numbers are needed. A number is a mathematical value. Different types of numbers are available in mathematics, such as Natural numbers, Whole numbers, Rational numbers, and Irrational numbers, Real numbers, etc. There are four number systems available depending upon different properties 

  1. Decimal Number System
  2. Binary Number System
  3. Octal Number System
  4. Hexadecimal Number System

Cube

A cube is a 3-dimension shape with sides of the same length, height, and width. In geometry, a cube has 6 sides or faces where all the faces are squares, 8 vertices, and 12 edges. It is also called a regular hexahedron. The volume of a cube is calculated as side3, i.e., (side × side × side) cubic units.

In arithmetic and mathematics, the third power of a quantity has termed the cube of that amount since the volume of a cube is represented in terms of an edge e, as e3. For example, if the edge of a square box is 5cm, then the volume of a cube is 5 x 5 x 5 = 125 cm3. Some of the examples of cubes in real life are dice, sugar cube, ice cube, Rubik’s cube, etc.

Cube of a number    

The product obtained by the number multiplied three times by itself is called the cube of a number. It can be represented as 23 = 2 × 2 × 2 = 8.

Cube root of a number 

The cube root of a number is a number the returns the original number when cubed. It is obtained by using a ‘radical’ symbol with a tiny 3. This is the “cube root” sign, which is the “radical” symbol (used for square roots) plus a tiny three to represent the cube root.

3

For example, the cube root of a number 3√125 = 5

The natural number is said to be a perfect cube if the number is multiplied by itself thrice. Perfect cubes are not defined for negative numbers just like the perfect square. The perfect cube numbers from 1 to 10 are 

13 = 1 × 1 × 1 = 1

23 = 2 × 2 × 2 = 8

33 = 3 × 3 × 3 = 27

43 = 4 × 4 × 4 = 64

53  = 5 × 5 × 5 =125

63 = 6 × 6 × 6 = 216

73 = 7 × 7 × 7 = 343

83 = 8 × 8 × 8 = 512

93 = 9 × 9 × 9 = 729

103 = 10 × 10 × 10 = 1000.

Some properties of the cube of a number

  • The cube of a negative number will always result in a negative number.
  • The cube of a positive number will always result in a positive number.
  • The cube of an even number is an even number.
  • The cube of an odd number is an odd number.

What is the Cube of (−3)?

The cube of a number is the number multiplied by itself thrice as mentioned earlier. for the negative numbers, cubes are negative since the negative numbers are multiplied thrice. When two negative numbers are squared, the result is positive. However, when the negative numbers are cubed, the result is negative 

(-3)3

= (-3) × (-3) = 9 

= 9 × (-3) 

= -27

Hence, the cube of (-3) is -27.

Similar Problems

Question 1: What is the cube of 12?

Solution:

123

= 12 × 12 × 12

=1728

Question 2: What is the cube of 10.5?

Solution:

10.53

= 10.5 × 10.5 × 10.5

= 1157.625

Question 3: What is the cube of -25?

Solution:

(-25)3

= -25 × -25 × -25

= -15625

Question 4: What is the cube of 197?

Solution:

1973

= 197 × 197 × 197

= 7645373

Question 5: What is the cube of -45.80?

Solution: 

(-45.80)3

= (-45.80) × (-45.80) × (-45.80)

= -96071.9119

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