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11.3 Simplifying Radicals

11.3 Simplifying Radicals Simplifying Radical Expressions

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Page 1: 11.3 Simplifying Radicals Simplifying Radical Expressions

11.3 Simplifying Radicals

Page 2: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplifying Radical Expressions

100 4 25 36 4 9

326

Product Property for Radicals

ab a b

10 2 5 36 4 9

Page 3: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplifying Radical Expressions

• A radical has been simplified when its radicand contains no perfect square factors.

• Test to see if it can be divided by 4, then 9, then 25, then 49, etc.

• Sometimes factoring the radicand using the “tree” is helpful.

Product Property for Radicals

50 25 2 5 2

14 7x x

Page 4: 11.3 Simplifying Radicals Simplifying Radical Expressions

Steps

1. Try to divide the radicand into a perfect square for numbers

2. If there is an exponent make it even by using rules of exponents

3. Separate the factors to its own square root

4. Simplify

Page 5: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify: 45

59

53

Page 6: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify: x49

x49

x7

Page 7: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify: t52

t134

t132

Page 8: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:12x

6x

26x

Square root of a variable to an even power = the

variable to one-half the power.

Page 9: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:88y

44y

Square root of a variable to an even power = the

variable to one-half the power.

Page 10: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:13x

xx6

12x x

112xx

Page 11: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:27x

13x x

26x x

Page 12: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:836x

46x

2 86 x

Page 13: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:1049y

57y

Page 14: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:645x

33 5x

69 5x

Page 15: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:750y

35 2y y

625 2y y

Page 16: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:948y

24 3y y

416 3y y

Page 17: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:1680y

84 5y

1616 5y

Page 18: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify: 363y

183y

Page 19: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify: 50202 2 xx

52 x

25102 2 xx

252 x

Page 20: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:2 6 9y y

3y

23y

Page 21: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify: 104 5x

52 5x

104 5x

Page 22: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify: 950 7y

45 7 2 7y y

825 7 2 7y y

Page 23: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:336x

6x x

Page 24: 11.3 Simplifying Radicals Simplifying Radical Expressions

Simplify:4 7448x y

2 38 7x y y

4 6 1124x y y2 32x y 4 28y 2 32 2x y 4 7y

Page 25: 11.3 Simplifying Radicals Simplifying Radical Expressions

Cube roots

• 2^3 = 8

• 3^3= 27

• 4^=64

• 5^3=125

• Classwork Page 494(2-16) even

Page 26: 11.3 Simplifying Radicals Simplifying Radical Expressions

Assignment:

Page 4932-48 (even other even)