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Chapter 10 Section 1
Square Root Property
Learning Objectives
Know that every positive real number has two
square roots.
Solve quadratic equation using the square root
property
Key Vocabulary
Quadratic Equation
Square Root Property
Quadratic Equation
 Standard form of a quadratic equation is
ax2 + bx + c = 0
 a, b, and c are real numbers and a ≠ 0
 a is the coefficient of the squared term
 b is the coefficient of the first-degree term
 c is the constant
 It is important to label the a, b and c with the correct sign when
substituting into the quadratic formula
Positive Real Numbers
 Every positive real number has two square roots
 Example
16  4 and
16  4 written as
16  4
because (4)(4)  16 and (4)(4)  16
Positive Real Numbers
 Example
25  5 and
25  5 written as
25  5
because (5)(5)  25 and (5)(5)  25
 Example
144  12 and
144  12 written as
144  12
because (12)(12)  144 and (12)(12)  144
Square Root Property
 If
x2 = a then
x a
or
x a
written as
x a
 Mostly used when an equations like x2 - 29 = 0 cannot be factored,
however it works on all equations in this form.
Solve:
x 2  49  0
x 2  49
x  49
x  7
2
Difference in two squares
x2 – 49 = 0
x2 – 72 = 0
(x – 7) (x + 7)
x – 7 = 0 and
x=7
and
x+7=0
x = -7
Square Root Property
Solve:
Solve:
x  19  0
x 2  23  58
x  19
x 2  58  23
2
2
x  19
2
x   19
x 2  81
x  81
2
x   81
x  9
Square Root Property
Solve:
Solve:
x  100  0
x  29  0
x  100
x  29
2
2
x  100
x  10
2
2
2
x 
2
29
x   29
Square Root Property
Solve:
 x  5
Solve:
2
x 2  5  20
 16
 x  5
2
x 2  20  5
 16
x  5  4
x  25
x  5 4
x 
2
2
x  5 4
and
x  54
x9
and
x 1
25
x   25
x  5
Square Root Property
Solve:
 x  3
Solve:
2
 3 x  2   4  28
2
 36
 x  3
2
 3x  2 
2
 3x  2 
2
 36
x  3  6
x3
 32
 3x  2 
x  3  6
x  3  6
 28  4
and
and
x  3  6
x  9
2

32
3x  2  
32
3 x  2 
32
3 x  2 
16
3 x  2  4
x
2  4
3
2
2
2
Square Root Property
Solve:
 4m  1  6  51
2
 4m  1
2
 4m  1
2
 51  6
 45
 4m  1
2
4m  1  

45
4m  1 
45
4m  1 
9
4m  1  3 5
x
45
1 3 5
4
5
Square Root Property
The length of a rectangle is 4.5 times the width. If the area of
the rectangle is 1152 cm2 find the length and width.
 4.5 x   x   1152
Let:
x = width
4.5x = length
area = (length)(width)
width = x = 16
length = 4.5x = 4.5(16) = 72
4.5 x 2  1152
1152
4.5
 256
x2 
x2
x2 
256
x   256
x  16
discard the -16
Remember
 The square root property is needed to solve equations like
x2 – 13 = 0 that cannot be factored
 When we evaluated a square root such as
the principle square root, 3
9 we found only
 When using the square root property we include both the
positive and the negative square root. We have to use ± sign
 When solving an application problem we sometimes find
solutions that are not true or does not make since and we have
to discard them.
HOMEWORK 10.1
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