Unit 4: Coordinate Geometry

Simplify Radical Expressions p. 144

Square Root

( ) – the 2nd root of a number or expression

If b = a2, then = a. In order to determine a square root, such as b, ask yourself, “What number times itself will result in b?”

 

Example:

Simplify.

1) = 5

2) = 5

3) = 5€

25

€

5*5

€

52

ADDITIONAL EXAMPLES P. 144

2.

€

1921.

€

47* 47

Simplify Radical Expressions

A square root can be simplified by extracting perfect squares.

Example

Method 1 Perfect Square Factors

Method 2 Perfect Squares Using the Factor Tree

€

20

Example p. 145

1) Priscilla used the factor tree to express a number as the product of its prime factors. The last line of her factor tree is shown. 2 • 3 • 2 • 5 • 3

How many perfect squares are factors of her number?

Simplify

€

2* 3*2*5* 3

Example 2 p. 145

2) Simplify .

€

72

ADDITIONAL EXAMPLES P. 145

Identify the perfect squares and simplify.

€

2) 3*5* 3* 3* 3*2€

1) 3*5* 7*5

Operations with Radical Expressions p. 146

Only like terms can be added or subtracted. Like terms have the same variable or radical components. 2 and 3 are not like terms and cannot be added or subtracted.

Rule: Simplify the expressions. Add or subtract the coefficients. Retain the variable or radical component of the terms.

Rule: Multiply or divide the coefficients. Multiply or divide the variable or radical components of the terms. The radical expressions do not have to be simplified first. Simplify the final answer.

Any terms can be multiplied or divided.

Examples p. 146

€

1)3 2 +5 2

2)3 2 +9 3 −5 2

3) 36 + 20 + 5 −2

EXAMPLES

€

4)6 10

2 2

EXAMPLES

€

5)40

5

6)3 6 *2 2

7) 89 * 89

ADDITIONAL EXAMPLES P. 146

€

1) 28 + 3 7 − 20

2) 6 2( ) 3 10( )

3)6 6

12 2