SQUARES

&

SQUARE ROOTS

•Squares: “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

Squares

Square RootsThe 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=9Try:

= 8, because 82=64

= 12, because 122=144

= 1, because 12 = 1

= 0, because 02 = 0

A Perfect Square: is “perfect” because its square root is a whole number.Example:

is a perfect square because = 7

Perfect Squares

49

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 = 6.3245…

40

Approximating Square Roots

You need to estimate its value of non-perfect squares by

determining which two whole numbers 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

√55 

√23

√5 

√14

√44

Find the two consecutive numbers the following non-perfect square fall between.

SHOW WORK!andandandandand

Between 7 & 8 Between 4 & 5 Between 2 & 3 Between 3 & 4 Between 6 & 7

Answer the following problem SHOW WORK!

1. I am a number. I am not zero. If I am squared, I’m still the same number. What number am I?

1

Answer the following problem SHOW WORK!

2. If a square bedroom has an area of 144 square feet, what is the

length of one wall?

12 feet

Answer the following problem SHOW WORK!

3. 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.

Answer the following problem SHOW WORK!

4. 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