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1.3 Applications of Square Roots
Page 30
Define the following:
1. Pythagorean Theorem-
2. Hypotenuse-
3. Pythagorean Triplets-
4. Principal square root-
A perfect square is a number that is a product of two identical factors.
Example: 16 is a perfect square because 16 = 4 x 4.
Finding the square root of a number is the inverse operation of squaring.
For example,
42
= 4 4
= 4
16 =
The Pythagorean Relationship
The Pythagorean Relationship can be used to find the lengths of the sides of
a right triangle. The longest side of a right triangle is called the hypotenuse.
The square of the length of the hypotenuse is the sum of the squares of the
two shorter side lengths.
c2 = a2 +b2
z 2 = x2 + y2
a)
b)
c2 = 52 +32
102 = 82 + y2
c2 = 25 + 9
100 = 64 + y2
c2 = 34
36 = y2
c2 = 34
y2 = 36
c=5.83
y=6
Notes
HOW CAN YOU FIND SQUARE ROOTS
1. Copy and Complete the table.
Perfect Positive Factors Negative Factors
Square as a Power
as a Power
2
1
1x1=1
(-1) x (-1) = (-1)2
4
2 x 2 = 22
(-2) x (-2) = (-2)2
9
3 x 3 = 32
(-3) x (-3) = (-3)2
16
25
36
Square Roots of
Perfect Square
1 or -1
2 or -2
3 or -3
Principal
Square Root
1
2
3
2. Extend the table to include perfect squares between 48 and 101.
3. Examine the patterns in the table. How many square roots does a
perfect square have? Describe the square roots.
4. Create another table similar to the one that you completed in
question1. Change the heading of the first column to Square Number.
Add the decimals 0.01, 0.04, 0.09, 0.16, 0.25, and 0.36 to the table.
Do these numbers follow the same patterns as the whole numbers?
Square
Number
0.01
0.04
0.09
Positive Factors Negative Factors
as a Power
as a Power
(0.1) x (0.1)= 0.01
2
(-0.1) x (-0.1)= (-0.01) 2
Square Roots of
Square number
0.1 or -0.1
Principal
Square Root
0.1
Example 1: Work with Square Root and Principal Square Root
a) Find the square roots of each mentally, where possible, or by using a
calculator.
i) 121
ii) 72
iii) 169
iv) -169
v)
4
9
b) You were told that 169 is the number of dollars you would earn for
walking Mr. Smith’s dog. How much would you earn?
c) x2 = 100. Solve for x.
Example 2: Apply Square Roots
A square floor tile has an area of 0.09 m2.
a) What are the dimensions of the tile?
b) You plan to cover a hallway measuring 3.33 m by 1.00 m in these
tiles. How Many tiles will you need?
HOMEWORK: Check Your Understanding Page 33 #1, 2, 3, 4, 5, 6, 7, 8