NUMBER

Square Numbers

Learn the reliable method for square numbers, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A square number is the product of an integer multiplied by itself.

Picture itBuild a square number
2 · THE METHOD

Follow these steps

  1. Identify the integer being squared.
  2. Multiply it by itself.
  3. Use known square-number facts to compare or complete a pattern.
3 · WORKED EXAMPLES

See the method in action

Example 1

Which value is equal to 5 squared?

  1. 5² means 5 × 5 = 25.
Answer: 25
Example 2

The difference between two consecutive square numbers is 19. What is the larger square number?

  1. Consecutive squares differ by (n + 1)² − n² = 2n + 1.
  2. Here, 2n + 1 = 19, so n = 9.
  3. The larger square is 10² = 100.
Answer: 100
4 · ELEVENSPRINT TIP

A useful shortcut

Use known square-number facts to compare or complete a pattern.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.