I’m struggling to see how when 2.5 is squared, the visual represetation shows two half squares on the side and the top? If you start with just two full squares and one half square and then when you double it, you just add on two more full squares and one more half square. Just like if 2 is squared, visually you would start with just two blocks and then double it which would result in the visual and mathematical output being the same.

Hi @donyd,

You can think of the number being squared as the side lengths of a square and the answer as the area of that square.

For example, let’s look at 3^2

The side lengths of the square are 3 by 3.

If you subdivide the square into individual units, you get 3 rows of 3 unit squares.

And if you count up those unit squares you have a total of 9.

Now let’s look at 2.5^2.

The side lengths of the square are now 2,5 by 2.5.

If you subdivide the square into individual units, you get 2.5 rows of 2.5 unit square.

If you add these up, you have 4 complete unit squares, plus 4 half squares, plus 1 quarter square.

The 4 half squares make 2 complete squares, so you end up with 6.25 total.

Doing the same thing with 3.5^2,

We now have 3.5 rows of 3.5 unit squares,

This gives us; 9 complete unit squares, 6 half-squares, and 1 quarter square.

So 9 + 3 + (1/4) = 12.25

I hope that makes sense but if you’re still struggling let me know and I’ll see if I can draw some diagrams for you.

Hi @garypettie I figured it out, but still appreciate the explanation. The issue was when visualising the squaring. When you start with 2^2 it kinda makes sense with the four squares but then the jump to 2.5^2 tripped me up. Just the way when four squares had green parts drawn in to show 2.5.

The way it made sense to me was starting off with two and a half squares and then doubling that, and then adding half of it the two and half squares to finish off the diagram.

I’m glad to hear that you worked it out. Apologies for being a little behind on the forum this week!

No worries, i’m sure you have a full plate. Thanks again.

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