Name:__________________________________________
Notes on Square Numbers
A square number, or a perfect square, is the number we get after multiplying an integer (a
number that is not a fraction) by _____________.
Example: 4 × 4 = 16, so 16 is a __________ number. Notice below that you can make a square
with 16 tiles.
Let’s use some tiles. Can you make a square with 12 tiles? __________Why not?
_____________________________________________________________________________
Can you make a square with 9 tiles? ____________ Why?
_____________________________________________________________________________
Starting with 1, here are the first few square numbers:
1
(1×1)
4
(2×2)
9
(3×3)
16
(4×4)
25
(5×5)
____ (6 x6)
____ (7x7)
____ (8 x 8)
____ (9x9)
____ (10x10)
"Squared" is often written as a little 2 like this:
You read this as "4 Squared equals 16"
(the little 2 is called an exponent. An exponent of 2 means that the number appears twice in
multiplying.
Here’s a trick for quickly finding square numbers. Look at the multiplication chart below.
Notice where the square numbers are!
Let’s practice.
a) 42 _____ b) 102 _____
g) 72 _____
l) 92 _____
h) 52 _____
m) 32 _____
c) 82_____
i) 152 _____
n) 22 _____
d) 122_____
j) 142 _____
o) 132 _____
e) 12 _____
k) 112 _____
f) 62_____
Now that we’re good at squaring numbers, let’s do the opposite. We are going to find the
___________ roots of numbers.
The square root, or radical, symbol looks like this: 
When you see that symbol in front of a number, you ask yourself, “What number times itself
gives me this number?”
Below are examples:
You can think of a square when finding the square root of a number. Let’s say you have 9 tiles.
How can you arrange those tiles into a square? Let’s try it.
Does your square look like this? Great job!
You can make a ____ by ____ square with 9 tiles. That means that the square root of 9 is _____.
Let’s practice on the next page.