Year 7 - Maths
Square and cube roots
Properties of number: factors, multiples, squares and cubes
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Study Guides
This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils develop their understanding of factors and multiples, then extend this knowledge to learn general divisibility tests for integers and develop strategies to determine the highest common factor and lowest common multiple of two or more integers.
Lesson Summary
You will learn to explain the concept of square root and cube root and calculate them.
Key Notes
- The square root of any perfect square will be an integer.
- The square root of any perfect square will be an integer and can be calculated by using trial and improvement.
- The cube root of any perfect cube will be an integer.
- The cube root of any perfect cube will be an integer and can be calculated by using trial and improvement.
Vocabulary To Learn
- Perfect square: A perfect square is the same as a square number.
- Perfect cube: A perfect cube is the same as a cube number.
- Square number: A square number is the product of two repeated integers.
- Cube number: A cube number is the product of three repeated integers.
Common Mistakes To Avoid
- The root of an integer is half of the integer.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The square root of any perfect square will be an integer. The square root of any perfect square will be an integer and can be calculated by using trial and improvement.
2. Use this key word in a maths sentence and explain it clearly. 'Perfect square'
A perfect square is the same as a square number. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: The root of an integer is half of the integer. Correction: The square root is the inverse of a square number. A square is the product of 2 repeated integers.
More Lessons In This Unit
- Calculating integers from their prime factor expressions Study Guide
- Checking understanding of factors, multiples, squares and cubes Study Guide
- Checking understanding of prime numbers Study Guide
- Divisibility tests for 2 and 3 Study Guide
- Divisibility tests for 4 and 8 Study Guide
- Divisibility tests for 5 and 10 Study Guide
- Divisibility tests for 6 and 9 Study Guide
- Expressing an integer as a product of its prime factors Study Guide
- HCF or LCM Study Guide
- Highest common factor Study Guide
- Listing factors Study Guide
- Listing multiples Study Guide
- Lowest common multiple Study Guide
- Power notation Study Guide
- Powers and roots using a calculator Study Guide
- Problem solving with factors, multiples, squares and cubes Study Guide
- Securing understanding of factors, multiples, squares and cubes Study Guide
- Square and cube numbers Study Guide
Browse all guides in the Year 7 Maths guide library.