Square x (x^2)

Intro

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Simplicity is often something not attributed to math, but squaring numbers should be.

Do you know why we say “the square of x is…”? It’s very simple, we are really saying “the area of a square with sides x is…”.

Remember that any rectangle has an area of its length times its height (area=(length)*(height)). And a square is simply a rectangle where the height and the length are the same! Thus a square has an area of length times length (or height times height depending on how you want to look at it). So a square has an area of its length squared (area=length^2)!

Let’s try it in a sample problem:

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Sample Problem

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Get a piece of paper and a pencil.

Draw a big square on the page. Within that square, make 4 lines equal distant apart. There should be 5 rectangles in the big square.

Now draw 4 more lines going perpendicular (the opposite direction of the other lines) from the first set of lines.

You should have a big square with 25 little squares in it.

The big square is 5 little squares long (length) by 5 little tall (height).
The area of the square then is 5 times 5 or 5^2 and as we know 5^2=25!

So x^2 is simply saying that the area of a square with sides x is…!

Remember x^2=x*x= the area of a square.

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Solution

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Notice that a square is x units tall, y units long, and x and y are the same distance (or x=y).

Now the area of a square is the length (how long it is) multiplied by the height (how tall it is). Thus area=x*y and since x=y we can rewrite that to say area=x*x or area=y*y.

area=x*x=x^2 or area=y*y=y^2

Therefore x^2 is the area of any square with side x.

If x=5 then 5^2=5*5=25 or the area of a square with side length 5!

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