Perfect Cube Definition

A perfect cube is a number that is the cube (raised to the power of 3) of an integer. For example, 8 is a perfect cube because it can be written as 2^3 (2 x 2 x 2). Some other examples of perfect cubes include 27 (3^3), 64 (4^3), and 125 (5^3).

Perfect Cube Definition

The equation of a perfect cube:

a^3 = aaa where a is a real number.

Note that not all integers are perfect cubes. For example, 7 is not a perfect cube because there is no integer that, when cubed, will equal 7. In other words, there is no integer “a” such that a^3 = 7.

In addition to being the cube of an integer, a perfect cube can also be expressed as the product of an integer and its square. For example, 8 is not only 2^3, but it is also (2 x 2) x 2.

There are also some mathematical properties associated with perfect cubes. For example, the sum of the digits of a perfect cube will always be divisible by 3 (this property is known as the “digital root” test). Additionally, the last two digits of a perfect cube will always be the same as the last two digits of the number being cubed. For example, the last two digits of 8^3 and 8 are both “64”.

In terms of algebraic equations, solving the equation x^3 = a, where a is a perfect cube, is easier than solving a general cubic equation. since, you can factor out x from the left hand side and get x(x^2)= a.

Perfect cubes are also important in number theory and also used in many combinatorial problems.

You can also check if a number is perfect cube or not by taking cube root of that number and check if it is an integer or not.

List of Perfect Squares
How Many Perfect Squares Between 1 and 100
Square Root Chart
Roman Numerals Chart
Odd and Even Numbers Chart
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How Many Grams in a Kilogram
How Many Ounces in a Pound
Decimal Place Value Chart