Algebra 12.2 Operations with Radical Expressions √

Algebra12.2

Operations with Radical Expressions √

Review: Simplifying √ Expressions

1. Factor terms under the radical.Find the largest perfect square factor(s).Take square roots outside.

2. Rewrite in simplified form.

72 2 36 6 2

240 2 2 2 2 3 5 4 15

Prime factorization can be useful

Warm-Up: You try.

28 4 7 2 7

84 2 2 3 7 2 21

90 9 10 3 10

150 6 25 5 6

5 2 7 3 8 2

Adding and Subtracting Radicals

You can add and subtract terms that have the same radicand.radicand

These are LIKE TERMS.

13 2 7 3

Add and Subtract: You try.

3 7 5 7 10 7 8 7

2 2 5 6 2 4 2 5

8 5 125 13 5

Simplify each radical term first

8 5 5 5

Add and Subtract: Simplify each term first.

4 3 27 300

11 3

4 3 9 3 100 3

4 3 3 3 10 3

50 2 2 25 2

5 2 2 6 2

Multiplying Radicals

12 5 3 305 36

6 4 10 6 5 8

12 10

6 40

1. Multiply terms outside the radical together.

2. Multiply terms inside the radical together.

3. Simplify.

5 6

6 2 10

Multiplying Radicals

You can multiply using distributive property and FOIL.

3 (7 3 )

5 2 4

7 3 3

(6 2 )(6 2)

2 (5 8)

34

36

5 2 16

6 2 6 2 2

36 2 It’s a DTS!

Multiply: You try.

5 (2 5 ) 2 5 5

2( 2 5 )

9 4 5

( 2 5 )( 2 5 )

4 2 5 2 5 5

(5 7 )(5 7)

It’s a PST!

25 7 18

Dividing to Simplify Radicals

2

32 3

3

3

3

No radicals in the denominator allowed

Denominators must be “rationalized.”

Multiply by 1in the form of

√

√

15

515 5

5

5

5 3 5

3

1

Using the Conjugate to Simplify

Conjugate The other part of a DTS

Expression Conjugate Product

( 2 5 ) ( 2 5 ) 4 5 1

(10 2 ) (10 2 ) 100 2 98

( 10 6) ( 10 6) 10 36 26

The radical “goes away” every time

Dividing to Simplify Radicals

2

5 310 2 3

25 3

5 3

5 3

Multiply by 1in the form of

5 3

11

conjugate

conjugate

10 2 3

22

5 1

11

Simplify: You try.

6

23 2

5

55

4

2 3 8 4 3

Summary:

To ADD and SUBTRACT COMBINE LIKE TERMS

To MULTIPLY “Outside” NUMBERS x NUMBERS

“Inside” NUMBERS x NUMBERS

DISTRIBUTE and FOIL

To DIVIDE “Rationalize” denominator using

1Use conjugate

ALWAYS SIMPLIFY AT THE END IF YOU CAN

Homework

pg. 719 #5-11 odd #19-49 odd