Perfect Squares & Square Roots
A perfect square is the product of an integer multiplied by itself. A square root asks which number was multiplied by itself to create a square.
So, 49 is a perfect square.
Because 7 × 7 = 49.
Learning Goals
Quick Reference
1²=1 · 2²=4 · 3²=9 · 4²=16 · 5²=25 · 6²=36 · 7²=49 · 8²=64 · 9²=81 · 10²=100 · 11²=121 · 12²=144 · 13²=169 · 14²=196 · 15²=225
Interactive Demonstration: Build a Square
Choose a whole number. The app will build an n by n square and show why the result is a perfect square.
Square Root Demonstration
Pick a perfect square and trace it backward to its square root.
Why Square Roots “Undo” Squaring
If 9² = 81, then √81 = 9. These operations reverse each other for nonnegative numbers.
Online Practice
Answer the questions, check your work, and open detailed explanations whenever you need them.
Score: 0 / 10
Challenge Mode
These questions include missing factors, comparisons, and reasoning.
Printable Practice Center
Create a worksheet and a separate answer-key sheet. The answer key includes worked explanations.
Customize the App
Choose a classroom-friendly theme and text size. Your choices are saved on this device.
Teacher Notes
This app is designed for whole-class demonstration, stations, independent practice, and take-home printable work.
Suggested Sequence
Begin with the visual square model, connect the model to multiplication, then reverse the process using square roots. Follow with online practice and finish with a printed mixed set.
Common Misconception
Students may confuse √64 with 64 ÷ 2. Emphasize that square root means “What number times itself equals 64?”
Tip: In full-screen mode, the app works well on interactive whiteboards and classroom displays.