Download 1.5 Simplify Square Roots and Solve.notebook

1.5 Simplify Square Roots and Solve.notebook
September 21, 2016
Warm Up
page 22
42. A rectangular picnic site measures 24 feet by
10 feet. You want to double the site's area by
adding the same distance x to the length and
the width. By what distance x should the length
and width be increased?
Warm Up Area Problem
√(x+5)
2
√(x-4)
2
Product/Quotient Props
1
1.5 Simplify Square Roots and Solve.notebook
September 21, 2016
Rationalize Denominator Containing Square Root
To rationalize transforms a fraction to an
equivalent form with NO radical in the denominator.
A. Single Radical Denominator
Steps:
1. Reduce the fraction, if possible.
Reduce like parts: radicand to radicand;
coefficient to coefficient
2. Multiply top and bottom by the square root in
the denominator.
3. Simplify top and bottom. Reduce again, if
possible.
Rationalize Denominators
Examples:
1.
2.
3.
4.
Rationalize Examples
2
1.5 Simplify Square Roots and Solve.notebook
September 21, 2016
Try these:
1.
2.
3.
4.
Practice
Multiply.
1.
2.
3.
4.
Binomial Denominators
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1.5 Simplify Square Roots and Solve.notebook
September 21, 2016
1.5 Solve by Square Roots continued
B. Binomial Denominator Containing Radical(s)
page 33
Examples:
1.
2.
Binomial Denominator
Examples continued:
3.
4.
More Binomial Denominators
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1.5 Simplify Square Roots and Solve.notebook
September 21, 2016
Try these:
1.
2.
3.
Practice Binomial Denominators
III. Solve Quadratic Equation By Square Roots
When solving a quadratic equation by square roots,
you are finding both the positive and negative roots.
If
NOTE:
then
To solve by square roots, you must
2
isolate x on one side of the equation.
Solve by Square Roots
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1.5 Simplify Square Roots and Solve.notebook
2
September 21, 2016
2
A. Form ax = c or ax - c = 0 (no bx term)
EXAMPLES:
2
4x = 240
2x
2
+ 5 = 167
Form ax squared = c
III. Solve Quadratic Equation By Square Roots continued
2
B. Form a(x-h) + k = 0
Still solving for x!!!
Isolate parentheses. Take square root of both sides.
Then add or subtract to isolate x.
EXAMPLES:
2
(x + 3) - 25 = 0
-2(x - 1)
2
+ 12 = 0
Form a(x­h) squared + k = 0
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1.5 Simplify Square Roots and Solve.notebook
September 21, 2016
Form a(x­h) squared + k = 0
Homework
page 35, problems 3-21 odd,
problems 22-33 all
Homework
7