*Joseph Vigil*Show bio

Joseph has a master's degree in literature as well as alternative teaching and ESL educator certifications. He has worked with middle school, high school, and college students in writing and language arts.

Lesson Transcript

Instructor:
*Joseph Vigil*
Show bio

Joseph has a master's degree in literature as well as alternative teaching and ESL educator certifications. He has worked with middle school, high school, and college students in writing and language arts.

In math, square numbers refer to the product of multiplying any integer by itself. Learn the complete definition of square numbers and why they are called 'square.' Calculate the given examples and find the square numbers!
Updated: 10/12/2021

So, what's so special about these square numbers? What makes 1, 4, and 9, for example, square? For a simple definition, **square numbers** are the results you get when multiplying any integer by itself. For example, let's multiply 1 by itself:

- 1 * 1 = 1

So, one is a square number. Simple enough, right? How about the next integer: 2?

- 2 * 2 = 4

So, four is the next square number. I'll bet you can probably guess how to find the next square number. That's right! Let's multiply 3 by itself:

- 3 * 3 = 9

And so on. . .

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Are you a student or a teacher?

Create Your Account To Continue Watching

As a member, you'll also get unlimited access to over 84,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Get unlimited access to over 84,000 lessons.

Try it now
Replay

Your next lesson will play in
10 seconds

Okay, that all makes sense. But, why do we call these numbers 'square?' Well, let's make a diagram of the previous multiplication sequence. If we're multiplying 3 by 3, that means we have 3 groups of 3 items.

As you can see, we have a grid measuring three items vertically and three items horizontally, and these items, when arranged in this way, make a square. We can add another row of items going both ways. The resulting diagram would look like this. We now have a square of 4 items vertically and 4 items horizontally, which gives us a total of 16 items (a square number).

So, now you have the tools to find every square number in existence. Just multiply any integer by itself, and the result is a square number. And, it's called a square number because we can make a diagram of that many items, and it will take the shape of a square.

But, how would this play out in the classroom? Let's say your teacher asks, 'What is 4 squared?' This is just another way of asking, 'What do we get when we multiply 4 by 4?' The result is 16.

It even works with big numbers. If we're trying to find 100 squared, we just multiply 100 by 100, and we get 10,000. Of course, the diagram of that square number would be quite large, but it would still work out as a square of 100 items across and 100 items down.

So, simply put, when you multiply any integer times itself, whether it be 1 or 1 million, the result is a **square number**. If you're looking for the square of any particular integer, simply multiply that integer by itself. If you're ever in doubt whether a number is a square number, try diagramming it. If you can place that many items into a square grid, you have a square number.

What is a Square | Examples |
---|---|

A square number is the result of multiplying a number by itself. | 4 is a square because 2 * 2= 4 9 is a square because 3 * 3= 9 |

After you've finished, you should be able to:

- Define and explain the concept of a square number
- Identify a square number
- Calculate small and large square numbers

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackRelated Study Materials

- Math Courses
- English Courses
- Standardized Tests Courses
- Teacher Resources Courses
- Study Courses
- AP English Literature: Homework Help Resource
- AP English Literature: Help and Review
- High School Geometry: Homework Help Resource
- High School Geometry: Help and Review
- High School Geometry: Tutoring Solution
- High School Trigonometry: Help and Review
- CSET Social Science Subtest II (115): Practice & Study Guide
- FTCE Middle Grades General Science 5-9 (004): Test Practice & Study Guide
- Praxis English Language Arts - Content & Analysis (5039): Practice & Study Guide
- CSET English Subtest IV (108): Practice & Study Guide
- NYSTCE English Language Arts (003): Practice and Study Guide
- Praxis Marketing Education (5561): Practice & Study Guide
- ILTS Social Science - History (246): Test Practice and Study Guide

- How Word Changes Indicate Parts of Speech
- How to Gather Knowledge About New Vocabulary Words
- The Albany Congress: Definition & Summary
- John White the Artist & Colonist: Paintings & Biography
- Henry Knox: Biography, Facts & Quotes
- Quiz & Worksheet - Continuity in a Function
- Quiz & Worksheet - Horizontal and Vertical Asymptotes
- Quiz & Worksheet - Slopes and Tangents on a Graph
- Quiz & Worksheet - How to Use Point-Slope Formula for the Equation of a Line
- Quiz & Worksheet - Implicit Functions
- Calculating Derivatives and Derivative Rules
- Graphing Derivatives and L'Hopital's Rule
- Applications of Derivatives
- Series
- Area Under the Curve and Integrals

- TExES Core Subjects EC-6 (391): Practice & Study Guide
- TExES School Counselor (252): Practice & Study Guide
- Virginia SOL - US History 1865 to Present: Test Prep & Practice
- Virginia SOL - US History to 1865: Test Prep & Practice
- Biology 202L: Anatomy & Physiology II with Lab
- Brief History of Life on Earth
- Evolutionary Theories
- Social Biology Behavior and Systems
- Ecological Models and Theories
- Earth's Climate and Composition
- Role of Student Support in Open & Distance Learning
- TExES Principal Exam Redesign (068 vs. 268)
- Teacher Salary by State
- ESL Resource Guide for Teachers
- What is a Homeschool Co-op?
- How to Start Homeschooling Your Children
- Addressing Cultural Diversity in Distance Learning

- Solving Quadratic Equations by Completing the Square
- Using Scientific Notation on a Scientific Calculator
- Bering Land Bridge: Evidence & Migration
- Using Trigonometry to Work With Vectors
- The Felder-Silverman Learning Styles Model
- Empresarios: Definition & System
- Goethe's Color Theory
- Quiz & Worksheet - For Loops in Python
- Quiz & Worksheet - Addition Rule for Limits
- Quiz & Worksheet - Addition & Subtraction Fact Families
- Quiz & Worksheet - Function Derivative Notation
- Flashcards - Real Estate Marketing Basics
- Flashcards - Promotional Marketing in Real Estate
- Relationship Skills Teaching Resources
- Calculus Worksheets

- CSET Social Science: Study Guide & Prep
- Organizational Behavior: Help and Review
- UExcel Anatomy and Physiology II: Study Guide & Test Prep
- ILTS Science - Earth and Space Science (108): Test Practice and Study Guide
- Basic Genetics for Teachers: Professional Development
- Terminology for the Gastrointestinal System
- FTCE Middle Grades English: Assessments of Learning
- Quiz & Worksheet - White Collar Crime
- Quiz & Worksheet - Violations of the Sherman Act
- Quiz & Worksheet - Linear Relationship Between Two Quantities
- Quiz & Worksheet - Agency Relationships
- Quiz & Worksheet - Issues of Parenthood During the Early Years

- Contract Labor: Definition & Laws
- Exogamy: Definition & Overview
- TExES School Counselor Exam Dates
- IELTS Speaking Section: Structure & Scoring
- Structure of the OET Speaking Section
- What GPA Do Colleges Look At?
- STAAR Test Taking Strategies
- Adjectives Lesson Plan
- Success Coaching with Study.com
- Bill of Rights Lesson Plan
- Pearl Harbor Lesson Plan
- Math Word Walls: Ideas & Vocabulary

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

- Is the following sentence a statement: This sentence is false or -2^2 = 4. Justify your answer.
- What is 5 squared by 2?
- How do I get 6.40 from b^2=41?
- What is 3 squared times 3 squared?
- What is 2.7 squared?
- What is 36 squared?
- What is 15 squared?
- What is 6 squared?
- What is 81 squared?
- Prove that for all integers ngeq 2, n^2 n+1.

Create an account to start this course today

Used by over 30 million students worldwide
Browse by subject

Upgrade to enroll

Upgrade to Premium to enroll in PSAT Prep: Tutoring Solution

Enrolling in a course lets you earn progress by passing quizzes and exams.

Track course progress

Take quizzes and exams

Earn certificates of completion

You will also be able to:

- Create a Goal
- Create custom courses
- Get your questions answered

Upgrade to **Premium** to add all these features to your account!

Upgrade Now
Upgrade to **Premium** to add all these features to your account!