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1 Warm-Up--March 18, 22, 2010 Simplify. 1. 2. 3. 4. 5.

Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

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Page 1: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

1

Simplify.

1. 2.

3. 4. 5.

Page 2: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

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Page 3: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

3

Section 5.6 Radical Expressions

Simplify:

28

81

32

Page 4: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

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VariablesSimplify:

x5 =

3 x10 =

4 x11y15 =

Page 5: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

5

Numbers and VariablesSimplify:

24a3b2 =

3 40x3y5 =

12m2n =

3 3 6 9n2 3 24n =

Page 6: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

6

Like Terms

+ =

+ =

Page 7: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

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Like Terms...in Algebra

2x + 5y + 7x + 8y =

4x2 + 5y + 7x3 + 9y =

Page 8: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

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Like Terms...in Algebra ...with Radicals

Page 9: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

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ADD/SUBTRACT Radical Expressions:

*Must be "like" radicals to add or subtract*The index number & the radicand must be the same to be "like" terms*Don't change the radical ­ add or subtract the numbers in front

Like or Unlike?

2 4 + 5 43 3

3 + 421 21

6x 5 + 4x 5x

Page 10: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

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ADD/SUBTRACT Radical Expressions:

*Simplify each term before adding or subtracting!

Examples:

4 + 3 5 + 7 + 2 5

4 27 + 3 3 ­ 48

Page 11: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

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MULTIPLY Radical Expressions:

*Multiply what's under the radical; then simplify

Examples:

10x2y * 40xy3

12m2n * 6mn2

6 3 * 3 3 9n2 24n

Page 12: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

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MULTIPLY Radical Expressions:

*Use the FOIL method

Examples:

(3 + 2)( 10 + 5)

(2 3 + 4 5)( 3 ­ 6 5)

(5 ­ 3)(5 + 3)

Page 13: Simplify. 1. 2. 3. 4. 5....PYTHAGOREAN THEOREM The measures of the legs of a right triangle can be represented by the expressions 6x2y and 9x2y. Use the Pythagorean Theorem to find

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