1. SQUARES
&
SQUARE ROOTS

2. Squares
Square of a number: “Squaring” a number means to raise a number to the second power.
Example:
4² = 4 · 4 = 16
9² = 9 · 9 = 81
16² = 16 · 16 = 256

3. Square Roots
The Square Root of a number is the number you can multiply by itself to give you that number.
Thus, = 2, because 22=4
= 3, because 32=9
Try:
= 8, because 82=64
= 12, because 122=144
= 1, because 12 = 1
= 0, because 02 = 0

4. Perfect Squares
A Perfect Square: is “perfect” because its square root is a whole number.
Example:
is a perfect square because = 49 7

5. Non-Perfect Squares
A Non-Perfect Square: is a number whose square root is NOT a whole number.
Example:
is NOT a perfect square because = 40
6.3245…

6. Approximating Square Roots
You need to estimate its value of non-perfect squares by determining which two perfect squares it falls in between.
Example:
11 is a non-perfect square
11 falls between perfect squares 9 & 16
Therefore, is between and
Since, = 3 and = 4
Then is between 3 and 4

7. Find the two consecutive numbers the following non-perfect square fall between. SHOW WORK!
√55 
√23
√5 
√14
√44
and
Between 7 & 8
and
Between 4 & 5
and
Between 2 & 3
and
Between 3 & 4
and
Between 6 & 7

8. Answer the following problem SHOW WORK!
I am a number. I am not zero. If I am squared, I’m still the same number. What number am I? 1

9. Answer the following problem SHOW WORK!
If a square bedroom has an area of 144 square feet, what is the length of one wall?
12 feet 9

10. Answer the following problem SHOW WORK!
An artist is making two stained-glass windows. One window has a perimeter of 48 inches. The other window has an area of 110 inches. Which window is bigger?
The window with a perimeter of 48 inches. 10

11. Answer the following problem SHOW WORK!
A square garden has an area of 225 square feet. How much fencing will a gardener need to buy in order to place fencing around the garden?
60 feet 11