11.3 Simplifying Radicals

Simplifying Radical Expressions

100 4 25 36 4 9

326

Product Property for Radicals

ab a b

10 2 5 36 4 9

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

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

Simplify: 45

59

53

Simplify: x49

x49

x7

Simplify: t52

t134

t132

Simplify:12x

6x

26x

Square root of a variable to an even power = the

variable to one-half the power.

Simplify:88y

44y

Square root of a variable to an even power = the

variable to one-half the power.

Simplify:13x

xx6

12x x

112xx

Simplify:27x

13x x

26x x

Simplify:836x

46x

2 86 x

Simplify:1049y

57y

Simplify:645x

33 5x

69 5x

Simplify:750y

35 2y y

625 2y y

Simplify:948y

24 3y y

416 3y y

Simplify:1680y

84 5y

1616 5y

Simplify: 363y

183y

Simplify: 50202 2 xx

52 x

25102 2 xx

252 x

Simplify:2 6 9y y

3y

23y

Simplify: 104 5x

52 5x

104 5x

Simplify: 950 7y

45 7 2 7y y

825 7 2 7y y

Simplify:336x

6x x

Simplify:4 7448x y

2 38 7x y y

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

Cube roots

• 2^3 = 8

• 3^3= 27

• 4^=64

• 5^3=125

• Classwork Page 494(2-16) even

Assignment:

Page 4932-48 (even other even)