1.5 Simplify Square Roots and Solve.notebook
September 20, 2016
WARM UP
Solve by factoring.
2
1. 4x = 24x
2
2. 16x - 361 = 0
2
3. 20x = 25x + 4
2
4. 2x + 7x - 15 = 0
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Homework Answers
1. x(x - 3)
2. (x - 10)(x + 10)
3. 4x(16x + 1)
4. 2(x - 10)(x + 10)
5. 2x(2x - 11)
6. (x - 6)(x + 6)
7. 4x(x - 4)
8. 2(12x
9. 3(2x - 5)(2x + 5)
10. 3x(3x - 1)
11. (x + 4)(x + 4)
12. (x + 9)(x - 1)
13. (x - 8)(x + 7)
14. (x + 4)(x + 10)
15. (x - 20)(x - 2)
16. (x + 9)(x - 6)
17. (2x + 7)(x + 1)
18. (2x - 3)(x + 7)
19. 3(2x + 1)(x - 1)
20. (2x - 3)(2x - 5)
21. 3(2x - 5)(x - 3)
22. 2(2x - 7)(x + 1)
2
- 23)
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1.5 Simplify Square Roots and Solve.notebook
September 20, 2016
Homework Answers continued
23. x = 6, -2
24. x = 8
25. x = 0, 9/10
26. x = 0, 3/16
27. x = 3, 4
28. x = -3, -5
29. x = -2/3, 3/2
30. x = 0, 49/16
31. x = 3/2, -4
32. x = 11, -9
33. x = 0, 2
34. x = -2/3, -3/5
HW Answers
Word Problems AGAIN!!
Doubling Area
page 20
Sep 15­7:32 PM
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1.5 Simplify Square Roots and Solve.notebook
September 20, 2016
Extra Example
You have a rectangular vegetable garden in your backyard that measures 15 feet by 10 feet. You want to double the area of the garden by adding the same distance x to the length and width of the garden. Find the value of x and the new dimensions of the garden.
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More Examples
page 22
43. A rectangular performing platform in a park
measures 10 feet by 12 feet. You want to triple
the platform's area by adding the same
distance x to the length and the width. Find
the new length and the width.
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1.5 Simplify Square Roots and Solve.notebook
September 20, 2016
Homework
page 29, problems 33-57 odd
page 23, problems 65-67
Sep 15­7:32 PM
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
Define Sq Root
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1.5 Simplify Square Roots and Solve.notebook
September 20, 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
√ 80
TRY!
√450
√72
Perfect & Non­Perfect Squares
page 32
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.
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1.5 Simplify Square Roots and Solve.notebook
√(x+5)
2
September 20, 2016
√(x-4)
2
Product/Quotient Props
6