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Perfect Squares

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Perfect Squares

Study Guide

Key Definition

A perfect square is a number that can be expressed as the square of an integer, such as $n^2$.

Important Notes

A perfect square is always non-negative.
The square root of a perfect square is an integer.
Examples include $4$, $9$, and $16$.
Perfect squares up to 100 are: $1, 4, 9, 16, 25, 36, 49, 64, 81, 100$.
The next perfect square after $100$ is $11^2 = 121$.

Mathematical Notation

$x^2$ denotes x squared

$\sqrt{x}$ represents the square root of x

$\times$ represents multiplication

Remember to use proper notation when solving problems

Why It Works

Understanding the concept of squaring is essential for solving quadratic equations and understanding geometric areas.

Remember

A perfect square results from multiplying an integer by itself, such as $n \times n = n^2$.

Quick Reference

First Perfect Squares:$1, 4, 9, 16, 25, 36, 49, 64, 81, 100$

Understanding Perfect Squares

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A perfect square is a number like $4$ or $9$ because $2 \times 2 = 4$ and $3 \times 3 = 9$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following is a perfect square?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If a square garden has an area of $64\, \text{m}^2$, what is the length of one side of the garden?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Find all integers which when squared give $49$.

Recap

Watch & Learn

Review key concepts and takeaways