Hey everybody! Sorry this is late.
OK, so we have 4 squares. Each square is made up of 100 little squares. Each large square is worth 1. That means that each little square would be worth 0.1. Our job is to find out how many perfect squares we can make out of the 4 large squares. A perfect square is a square in which the side lengths are whole numbers. (Numbers without decimals). Our job after that is to find the side length of a square that uses 2 large squares, 3 large squares, and 5 large squares. So, let's find out! :)
We started out with 1 large square. It's area is 1. This makes it a perfect square because 1 is a whole number. Our next biggest square would have an area of 1.21 because we are adding 21 little squares. (11 on the side, 1o on the top). In order to find the area of a square, you multiply the side length by itself. This would not be a perfect square because 1.21 is not a whole number. Here are the next biggest squares up to 4:
The only perfect square out of all of those numbers is 4. That means that you can only make 2 perfect squares using 4 large squares.
Now, let's find some side lengths!
2 squares: The side length using one square is 1. If we keep adding to that until another square is used up, we will get a side length of 1.4. (14 little squares on each side).
3 squares: The side length using 2 squares is 1.4. If we keep adding to that until we have used up another square we will get a side length of 1.7. (17 little squares on each side).
5 squares: Earlier, we found out that the area for 4 squares is 4. That means that we have to find out the square root of 4 in order to find the side length. That's easy because everybody should know that 2 x 2 = 4. That means that the side length using 4 squares is 2. If we keep adding to that until we have used up another square, we will get a side length of 2.24. (aprox. 22 little squares on each side).
Thanks for reading!