Download Lesson 1.4 Estimating Square Roots.notebook

Lesson 1.4 Estimating Square Roots.notebook
Sec 1.4
September 24, 2012
Estimating Square Roots
2. If the side length of a square is 4 cm,
what is the area of the square?
Pages 22-27.
First, some quick review.
1. If the area of a square is 36 cm2 , what is the side length of
the square?
4cm
Area
4cm
?
36cm2
side length =
= length x length
= 4cm x 4cm
= 16cm2
?
=
?
Aug 27­6:58 PM
Aug 27­7:04 PM
Estimating Square Roots that are non-perfect.
3. If the area of a square is 30 cm2, what
is the side length of the square?
A non-perfect square is a number that cannot
be written as a product of two equal numbers.
In the next example 30 is a non-perfect square.
Perfect
9
Perfect
25
Non-perfect
30
Aug 27­6:58 PM
Perfect Squares
1
Between which two consecutive perfect
4
squares does 30 fall ?
9
16
25
30 is halfway between 25
36
and 36 so answer is about 5.5
49
64
81
100
121
This is the perfect square method of
144
approximating a square root for a
169
non-perfect square.
196
225
. . . etc
25 = 5
36 = 6
Sep 14­11:23 PM
? 30cm2
side length
=
= ???
?
This is not a perfect square so we can‛t get
an exact answer.
But we can estimate using the perfect
squares we do know.
Aug 27­7:07 PM
Now, let's use the Numberline Method
to find square roots that are not perfect.
First we draw a number line and record the perfect
square less than our number and the perfect square
more than our number.
For 30 the perfect square below is 25 and
the perfect square above is 36.
Sep 14­11:31 PM
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Lesson 1.4 Estimating Square Roots.notebook
September 24, 2012
Example 2: Use the number line method to show the estimated value of each square root.
25
36
5
5.5
is 5 away from 6
a) 10
3
41
b)
4
c)
5
31
d)
56
6
7
8
and 6 away from Since these numbers are almost the same distance away, would be close to the middle of these two numbers. Since is closer to we can say
is approximately 5.4.
Sep 14­11:44 PM
Example 3: Is the whole number less than, equal to or greater than
the given square root?
Aug 27­7:16 PM
Example 4: Which whole number is closest to?
a) 5 or b) 9 or Sep 15­12:26 AM
Example 5: What is the approximate side length of a square with an area of 56 cm ? Give the answer to one decimal place. Use a calculator. Sep 23­9:54 PM
Prime Factorization
to estimate square root
1. Factor the number into prime factors
2. Combine pairs
3. Multiply ONE from each pair together to get answer.
So, 36 = 6
Sep 23­9:58 PM
Sep 15­12:33 AM
2
Lesson 1.4 Estimating Square Roots.notebook
Do this one:
1. Factor the number into prime factors
2. Combine pairs
3. Multiply ONE from each pair together to get answer.
Sep 15­12:38 AM
September 24, 2012
Complete questions on pages 25­27: #'s 4 , 5 and 7 a) with class. Assign 7 b, 8 a, 8 b, and 8 d for seatwork.
Homework: Use your calculator to estimate square roots in # 12, 13, 16, 17.
Now you can estimate square roots using:
1. Blocks or grid paper
2. Perfect squares
3. Number lines
4. Calculator or 5. Prime factors (Factoring & combining pairs)
Sep 14­11:18 PM
3