When no whole number fits

You have 20 tiles to lay in a square. Four rows of four use 16. Five rows of five need 25.

Rule: Square the whole numbers in order. Stop when a square is bigger than your number. Your number sits between that square and the one before it.

• 20 → between 16 and 25 → side between 4 and 5
• 30 → between 25 and 36 → side between 5 and 6
• 300 → between 289 and 324 → side between 17 and 18
• 3000 → between 2916 and 3025 → side between 54 and 55

A garden plot has area 90 m², that is 90 square metres. 9 × 9 = 81 fits inside the plot. 10 × 10 = 100 does not. So the biggest square bed with a whole side is 9 m.

Let n be any whole number. Going from n² to (n + 1)² adds 2n + 1. The last of those is (n + 1)² itself. So 2n numbers lie between n² and (n + 1)². For n = 20, that is 40.

Slide the number. See which two squares it sits between.

Try the lab to finish this lesson.