You may also like

problem icon

Cuisenaire Rods

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

problem icon

Making Boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

problem icon

A Right Charlie

Can you use this information to work out Charlie's house number?

Seven Square Numbers

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Seven Square Numbers


several numbers ranging from 1 to 19. 13 squared = 169 given and 5 squared = 25 given

Add the sum of the squares of four numbers between $10$ and $20$ to the sum of the squares of three numbers less than $6$ to make the square of another, larger, number.


Why do this problem?

This problem is suitable for learners who need a challenge when working with square numbers.

Key questions

Have you made a list of squares of the relevant numbers?

Have you remembered that $1$ is a square number?

What is the square root of that number?

Possible extension

Learners who need even more of a challenge could try Cycling squares.

Possible support

Suggest making a list of squares of the relevant numbers, remembering that $1$ is a square number.