Transcript Squaring

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,
Try:
= 2, because 22=4
= 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 nonperfect 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 7 & 8
√23
and
Between 4 & 5
√5
and
Between 2 & 3
√14
and
Between 3 & 4
√44
and
Between 6 & 7
ESTIMATING
SQUARE ROOTS
 Not
all numbers are perfect squares.
 Not every number has an Integer for
a square root.
 We have to estimate square roots for
numbers between perfect squares.
ESTIMATING
SQUARE ROOTS

To calculate the square root of a nonperfect square
1. Place the values of the adjacent
perfect squares on a number line.
2. Interpolate between the points to
estimate to the nearest tenth.
ESTIMATING
SQUARE ROOTS

Example:
27
What are the perfect squares on
each side of 27?
25
30
35 36
ESTIMATING
SQUARE ROOTS

Example:
half
5
25
30
27
6
35 36
27
Estimate
27 = 5.2
ESTIMATING
SQUARE ROOTS

 Estimate:
27
Example:
= 5.2
 Check: (5.2) (5.2) = 27.04
27
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 stainedglass 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
Homework
PAGE 29, #8-13
PAGE 30 14-26