How to teach square numbers and square roots
Year 7 (ages 12 to 13)
A square number comes from multiplying a whole number by itself (3 x 3 = 9). A square root undoes this: the square root of 9 is 3. This unit covers finding squares and roots of perfect squares, and estimating roots of numbers that are not perfect squares.
How to teach it
- Build square numbers concretely first: an n by n grid of squares has n^2 squares in total.
- Teach square roots as the inverse operation: 'what number, multiplied by itself, gives this?'
- Memorise the perfect squares from 1 to 20 (1, 4, 9, 16, 25... 400) as a foundation for quick root-finding.
- For a non-perfect square, find the two consecutive perfect squares it falls between to estimate its root.
- Connect squares to area (a square with side length n has area n^2) to keep the concept concrete.
Worked example
Find sqrt(64) 8 x 8 = 64, so sqrt(64) = 8
Common mistakes
- Confusing squaring (multiply a number by itself) with doubling (multiply by 2).
- Assuming every square root is a whole number, when only perfect squares have whole-number roots.
- Estimating a root by rounding the number itself rather than comparing it to nearby perfect squares.
- Forgetting that a square root has both a positive and (mathematically) a negative root, even though this unit focuses on the positive root.
Frequently asked questions
What is a square number?
A square number is the result of multiplying a whole number by itself, such as 4 (2x2), 9 (3x3) or 16 (4x4). These are also called perfect squares.
What is a square root?
The square root of a number is the value that, multiplied by itself, gives that number. The square root of 25 is 5, because 5 x 5 = 25. Square roots undo squaring.
How do you estimate the square root of a non-perfect square?
Find the two perfect squares it sits between. Since 6^2=36 and 7^2=49, sqrt(45) is between 6 and 7 (closer to 7, since 45 is closer to 49).
What year are square numbers and square roots taught?
In the Australian Curriculum this is a Year 7 skill (AC9M7N01), which describes how squaring and square roots are linked and uses them to solve problems with perfect squares.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.