Square Roots and Cube Roots – Side of a Square and a Cube
MathematicsNumbers & ArithmeticAges 14–15
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Numbers & Arithmetic
A square with area S has side √S; a cube with volume V has side ∛V. Drag the square's corner or the cube's vertex to change S and V and watch the side update; the bounding panel estimates each root by squeezing it between two integers and then refining one decimal digit at a time, the same method used in the textbook.
Lesson: Square roots and cube roots of a number; estimating root values
What it shows
The square root of a number S is the non-negative number whose square is S, so it is the side of a square with area S; the cube root of V is the edge of a cube with volume V. Perfect squares such as 25 or 64 and perfect cubes such as 27 or 125 give whole-number sides; other values give irrational roots that must be estimated. Bounding first traps the root between two consecutive integers by comparing squares or cubes, then narrows the interval one decimal place at a time, which is how √10 ≈ 3.16 can be found without a calculator.
How to use
Set Square area S to a perfect square, then to a value such as 10 or 50, and ask students to predict the side before reading it. With Show bounding/estimation steps on, click Next bounding step to reveal one inequality at a time, or Show all steps to check a prediction. Increase Number of decimal places when bounding to add digits. Repeat with Cube volume V and compare how side and edge grow.
Parameters you can change
- Square area S 1–100 cm²
- Cube volume V 1–125 cm³
- Number of decimal places when bounding 1–3
- Show bounding/estimation steps
Questions to explore
- Between which two consecutive whole numbers does √50 lie, and how can you tell without a calculator?
- If the area of the square is multiplied by 4, by what factor does its side change?
- By what factor must the volume of the cube be multiplied to double its edge?
