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September 28, 2016
Warm Up
Solve by factoring.
2
1. 4x = 24x
2
2. 16x - 361 = 0
Warm Up
page 22
2
3. 20x = 25x + 4
2
4. 2x + 7x - 15 = 0
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?
1.5 Solve Quadratics by Square Roots
I. Square Root of Positive Number
2
A number r is a square root of s if r = s
2
iff r = s
radical sign
radicand (number under the radical sign)
A positive number has TWO square roots:
and
2
= 10, since 10 = 100
2
= -10, since (-10) = 100
Untitled3665.notebook
September 28, 2016
To simplify a radical (if you do not know the
root/answer), factor the radicand using prime factors
prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, etc.
examples: √196
page 32
√ 80
A square root is simplified when:
1) the radicand has NO perfect square factors
other than 1,
2) the radicand is NOT a fraction, and
3) NO radical is in the denominator.
TRY!
√450
√(x+5)
2
√72
√(x-4)
Warm Up
2
1.
2.
3.
4.
5.
6.
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September 28, 2016
Rationalize Denominator Containing Square Root
Examples:
1.
2.
3.
4.
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.
Multiply.
Try these:
1.
2.
1.
2.
3.
4.
3.
4.
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September 28, 2016
1.5 Solve by Square Roots continued
B. Binomial Denominator Containing Radical(s)
page 33
HOMEWORK ANSWERS
1.
2.
3.
4.
5. skip
6.
Examples:
7. skip
8. x - 4
9. 3(x + 5)
1.
10. skip
11.
12.
13.
14.
15.
16.
Examples continued:
Try these:
3.
4.
1.
2.
3.
2.