[Maths Class Notes] on Perfect Cube Root Pdf for Exam

A perfect cube is the result of multiplying the same integer three times. Repeating the number 4 times three makes 64 and as a result 64 is a perfect cube.  64 has a cube root of 4. If a number can be decomposed into a product of the same three numbers, it is said to be a perfect cube.

A complete cube is the product of three identical numbers. To see if the number (for example n) is a suitable cube,multiply it by three times and check if the resulting number is the same as ‘n’ if yes then it is a perfect cube

One, eight, twenty-seven, and sixty-four are examples of perfect cubes. A perfect square is one that can be made by multiplying two numbers together. Both positive and negative numbers can be used to make perfect cubes. Because it is the product of multiplying -4 three times, -64 is a perfect cube.

When we say a number has been cubed, we mean that it has been multiplied three times. The process of cubing a number  is reversed by its root. When the number 5 is cubed, for example, we obtain 55 5, which is 125. The cube  root of 5 is 125. This is because multiplying the number 5 three times gives the result of 125.It is the same as the square root symbol with an addition of ‘3’ to indicate it is a cube root .The cube root of a number can be stated in exponent form as (number)13.

Cube root table

Cube root table is a table consisting of a list of numbers and their cube roots. Before we write the cube root table, it is very important for all of us to understand what is the perfect cube root chart and cube of a number. The cube of any real number can be defined as that number which is obtained by multiplying a number by itself twice or by raising its power to 3. At the same time, the cube root of any number is that number which when raised to the power 3 gives the answer as the number whose cube root is to be determined.

Perfect Cube Root Chart

Cube root of a number can also be exponentially represented as the number raised to the power ⅓. If ‘x’ is any real number, then its cube root is represented as (x)⅓  or ∛x. Perfect cubes are the numbers that are obtained when natural numbers are multiplied by itself twice. All the perfect cube numbers have a square root equal to a natural number. The perfect cube root chart of the first 25 perfect cube numbers is represented in the table below. 

While it is very important to know the cube roots of the numbers, it is also very important to know the table of cubes from 1 to 50 (i.e. first 50 natural numbers) in order to make our Mathematical computations easy and efficient without a calculator. The table of cubes from 1 to 50 is given below for the reference of students and facilitators. 

Table of Cubes from 1 to 50

Any student or a facilitator who is keen about Mathematics will find his or her own ways to memorize the cube root list 1 to 100. Though it may seem a little difficult at the initial days, the task of remembering the cube root list 1 to 100 becomes more and more easy through continuous practice and periodic revision. 

Cube Root List 1 to 100

Steps To Find Out Perfect Cube Root 

Following the steps below, you can check if a number is a perfect cube:

Step 1: Starting with the smallest prime number, prime factorise the given number (2).

Step 2: Once the prime factorization is complete, group together all three identical factors.

Step 3: Repeat Step 3 for all sets of the same three factors in the group. The provided number is not a perfect cube if any factors are left over that do not fit into a group of three identical factors. The provided integer is otherwise a perfect cube.

Fun Fact About Cube Root 

There is a method for determining whether or not greater integers are perfect cubes. To check, find the sum of the number’s digits repeatedly and see if it’s either 0, 1, 8, or 9. If it’s any of these, it could be a perfect cube, although that isn’t always the case.

Perfect Cube Formula 

The perfect cube formula is used to determine whether or not a number is a perfect cube. Let’s say we have a number, x, that equals yyy. Every composite number can be written as the product of the powers of its prime elements, according to the fundamental theorem of arithmetic. The number is considered to be a perfect cube if the power of all prime factors is a multiple of three.

From 1 to 50, this is a list of perfect cubes.

In the table below, the perfect cubes of integers 1 to 50 are presented. Every integer is multiplied three times by itself to get the ideal cubes.

Conclusion

This is how we can easily calculate perfect cube roots of different numbers. Focus on the concept of perfect cube roots and understand how they are determined. Follow the examples given in the tables and charts here to develop your conceptual foundation.