Square roots and cube roots – Grade 8 math lesson
Lesson 4 of 16 in the Grade 8 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 8 (ages 13–14) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 8 (ages 13–14)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Between which two whole numbers is √90? How do you know?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Thinking √16 = 8. The square root times itself must give 16: 4 × 4.
- Forgetting the negative square root when solving x² = 25. Both 5² and (−5)² are 25.
Tip for home: Use a calculator to explore roots of numbers that are not perfect squares.
What your child will learn
Learning goal: find squares, cubes, square roots and cube roots and estimate roots.
Success looks like
- I know squares and cubes.
- I can find square and cube roots.
- I can estimate roots.
Key words
- square root
- a number that squares to give the original
- cube root
- a number that cubes to give the original
- perfect square
- a whole number squared
- estimate
- a careful approximation
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Build squares from tiles and find the side length of squares with 36, 49 and 64 tiles.
The big ideas (for the adult)
Squaring multiplies a number by itself; the square root undoes it: √49 = 7. Every positive number has two square roots, +7 and −7.
Cubing multiplies three times; the cube root undoes it: ∛64 = 4.
To estimate a root, find the square numbers either side: √50 is a bit more than 7 because 7² = 49.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 8 math lessons
- Repeating decimals
- Scientific notation
- Laws of exponents
- Simplifying expressions
- Solving equations
- Systems of equations
- Arithmetic and geometric sequences
- Linear functions and slope
- Functions
- Graphing functions
- Angle relationships
- Volume and surface area
- The Pythagorean theorem
- Transformations
- Scatter plots and lines of fit
Curriculum
Common Core State Standards 8.EE.A.2: “Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.”
Common Core State Standards 8.NS.A.2: “Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.