Square Roots and Cube Roots
A square root is a number that multiplies by itself to give the original, and a cube root does the same with three equal factors.
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A square root is a number that multiplies by itself to give the original, and a cube root does the same with three equal factors.
- The square root of 49 is 7
- The cube root of 27 is 3
- Square roots of non-squares are irrational
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Square Roots and Cube Roots?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Square Roots and Cube Roots. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Square Roots and Cube Roots in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Square Roots and Cube Roots gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Square Roots and Cube Roots in detail
A square root of a number is a value that multiplies by itself to give that number, so √49 = 7 because 7 × 7 = 49. Every positive number has two square roots, one positive and one negative, though the √ symbol means the positive one. A cube root, ∛, is the number that multiplied by itself three times gives the original, so ∛27 = 3.
Knowing the square numbers up to 15² and cubes up to 5³ helps with estimating roots such as √50, which lies between 7 and 8. Roots are the inverse of powers and appear in Pythagoras' theorem, area problems and the quadratic formula.
How the interactive helps you understand Square Roots and Cube Roots
Watch the right-angled triangle in the interactive. Use any sliders or buttons it offers to change the values and see how the right-angled triangle responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Square Roots and Cube Roots.
Real-life uses and examples
- Spot Square Roots and Cube Roots in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Square Roots and Cube Roots by estimating first, then working it out step by step.
- Use Square Roots and Cube Roots when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Square Roots and Cube Roots.
- Memorising the steps for Square Roots and Cube Roots without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Square Roots and Cube Roots
What is Square Roots and Cube Roots?
A square root is a number that multiplies by itself to give the original, and a cube root does the same with three equal factors.
What are the most important points about Square Roots and Cube Roots?
The main points are: The square root of 49 is 7; The cube root of 27 is 3; Square roots of non-squares are irrational.
Why is Square Roots and Cube Roots useful?
Understanding Square Roots and Cube Roots gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Square Roots and Cube Roots?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Square Roots and Cube Roots?
Related topics in Mathematics include Rational and Irrational Numbers, Sets and Venn Diagrams, Geometric Sequences.