Exponents, Squares and Cubes

Go back to  'Algebra'

Introduction to Exponents, Squares and Cubes

Let us begin with what you know. You can easily write 2 x 2 = 4 without much difficulty, or even 3 x 3 x 3 = 27, however, what do you do when you need to represent 2 multiplied 10 times to itself?

That's a tough one right, only if you have not known about exponents, squares and cubes.

Mathematicians have already faced and addressed this particular hurdle and that brings us to the topics of exponents, squares and cubes.

The Big Idea: What are Exponents, Squares and Cubes?

Exponents, squares and cubes are a mathematical tool to express and calculate higher arithmetic calculations and also, find significant application in basic, intermediate and advanced abstraction.

An Exponent is a way to represent repeated multiplication of a number/variable with itself.

Squares and Cubes are limiting cases of exponents where the exponent component is always 2 or 3 respectively.

As now you have understood about the exponents and what does it mean, let us jump into an intresting topic related to it.

Square Roots

Just like how squares represent a number or variable multiplied by itself twice, a square root stands for the number that needs to be multiplied twice to get that particular number. Essentially it is the inverse operation of a square.

In an equation, a square root is represented by the following symbol;

Note: Numbers which yield whole numbers when their square roots are calculated are called Perfect Squares.

You can visualize square roots and know all about them using a fun tool below.

As, now we clearly understood about square roots, there is a similar topic known as cube roots.

Cube Roots

Similar to square roots, cube roots are the inverse operations of cubes. So, if a cube represents a number multiplied by itself thrice, the cube root of a number represents the number that is multiplied 3 times to give the original number.

The symbol that represents a cube root in an expression is as follows;

A number that yields a whole number when its cube root is calculated is called a Perfect Cube.

Here are few Questions for you to practice.

Activity Name Sup_ Exponents, Squares and Cubes_Activity
Item Name 1 Sup_Square_Item1
Item Name 2 Sup_Square_Item2
Item Name 3 Sub_Cube root_Item3
Item Name 4 Sub_Cube root_Item4









How do I understand

The Foundational Nature of Exponents, Squares and Cubes

People also ask for

Q) What is a cube squared?

 A) Cube numbers. A cube number is a number multiplied by itself 3 times. This can also be called 'a number cubed'. The symbol for cubed is ³. 2³ = 2 × 2 × 2 = 8.


Q) What comes after square and cube?

 A) 2 means square root, 3 means cube root. After that they are called the 4th root, 5th root and so on. If this is missing, it is assumed to be 2 - the square root.


Q) What is 4th power called?

 A) fourth power: biquadrate; biquadratic; fourth power; quartic.

How to Teach Your Child Exponents, Squares and Cubes

Exponents, squares and cubes further advances the applications of arithmetic and finds widespread use in abstraction as well. That’s why it is critical that children understand the concepts at play that govern these operations. Here are a few methods that will ensure that your child masters these operations:

Chunking: An age-old practice that has survived the test of time due to its effectiveness in helping children grasp new concepts by platforming off old ones. So, in your child’s study routine for exponents, squares and cubes, dedicate a certain amount of time for them to review older concepts from multiplication, division and basic algebra.

Flash Cards: These are an excellent tool to allow your child to have all the important concepts of a topic at their fingertips. Instruct them to practice answering both conceptual and arithmetic problems using timed flash cards to not only juggle their concepts, but also aid in their mental math abilities.

Important Topics

Learn from the best math teachers and top your exams

  • Live one on one classroom and doubt clearing
  • Practice worksheets in and after class for conceptual clarity
  • Personalized curriculum to keep up with school