Squares and Square Roots: Year 7 Guide
30 October 2026 · Pi Leo Academy
Does 6 squared mean 6 × 2 or 6 × 6? That small symbol can cause a surprisingly big mix-up. This Year 7 lesson makes squares and square roots easier to understand by connecting the numbers to something you can draw: a square made from equal rows.
You do not need to memorise a long list before you begin. Start with the picture, explain what it shows, and use multiplication to check your answer.
Watch the lesson
Watch this Pi Leo Academy lesson on YouTube. Pause whenever you want to try a step yourself.
What does “squared” mean?
A square array with 6 rows and 6 dots in every row contains 36 dots. We write this as 6² = 6 × 6 = 36. The small 2 tells you to multiply 6 by itself. It does not tell you to double 6.
The same idea works for area. A square with side length 6 cm has an area of 36 cm². The side uses centimetres; the area uses square centimetres because it counts unit squares covering the surface.
A square root works backwards
Suppose a square has an area of 144 cm². You want the length of one side. Ask: “Which nonnegative number multiplied by itself gives 144?”
- Recall that 12 × 12 = 144.
- Write √144 = 12.
- The side length is 12 cm.
- Check by squaring: 12² = 144, which matches the given area.
The square-root symbol √ gives the nonnegative root. Although (−12)² also equals 144, a side length cannot be negative. This distinction becomes useful when you later solve equations such as x² = 144.
Spot the growing pattern
Draw a 4-by-4 square and grow it into a 5-by-5 square. The number of dots increases from 16 to 25, so you add 9 dots. The next square has 36 dots, adding 11 more. Consecutive square numbers grow by successive odd numbers.
Drawing the extra row and column helps explain the pattern. Remember that their shared corner is counted only once. For more examples, open the matching squares and roots study note.
Two quick questions
- A square array has 8 rows of 8 counters. How many counters are there?
- A square has an area of 169 cm². What is its side length?
Answers: 1. 8 × 8 = 64 counters. 2. √169 = 13 cm, because 13 × 13 = 169.
A useful habit: Say the operation aloud before calculating: “square 8” means 8 × 8; “find the square root of 169” asks which number gives 169 when squared.
Your matching study notes
Use these notes alongside the video to revisit the method and practise at your own pace. Full notes and PDF downloads require an eligible Pi Leo Academy membership and sign-in.
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