Square roots and cube roots – Grade 11 math lesson
Lesson 5 of 23 in the Grade 11 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 11 (ages 16–17) 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 11 (ages 16–17)
- 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 11 math lessons
- Complex numbers
- Radicals
- Vectors
- Laws of exponents
- Systems of equations
- Rational expressions and polynomials
- Arithmetic and geometric sequences
- Iteration
- Functions
- Graphing functions
- Exponential functions
- Trigonometric functions
- Law of sines and law of cosines
- Coordinate geometry
- Counting outcomes
- Experimental probability
- Compound events
- Conditional probability
- Expected value
- Box plots and interquartile range
- Scatter plots and lines of fit
- Sampling and making inferences
Curriculum
Common Core State Standards HSN.RN.B.3: “Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.”
Common Core State Standards 8.NS.A.1: “Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.