Squares and Square Root 2 PowerPoint

SQUARES
&

SQUARE ROOTS

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

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

Try: = 3, because 32=9

= 8, because 82=64

= 12, because 122=144

= 1, because 12 = 1

= 0, because 02 = 0

Perfect Squares

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

Example:

49 is a perfect square
because =7

Non-Perfect Squares

A Non-Perfect Square: is a
number whose square root is
NOT a whole number.

Example:

40 is NOT a perfect square
because = 6.3245…

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

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

between. SHOW WORK!

√55 and Between

√23 and Between
√5 and Between
√14 and Between

√44 and Between

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

between. SHOW WORK!

√55 and Between 7 & 8

√23 and Between 4 & 5
√5 and Between 2 & 3
√14 and Between 3 & 4

√44 and Between 6 & 7

Using a Number line to find square
roots.

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?

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?

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?

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?

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