5-5 roots of real numbers objective: to simplify radicals having various indices, and to use a...

5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study Guide #

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5-5 Roots of Real NumbersObjective: To simplify radicals having

various indices, and to use a calculator to estimate the roots of numbers.

HW: 5-5 Study Guide #

Drill #56Factor the following polynomials

9124.3

44.2

168.1

Page 3: 5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study

Tourism

Open books to page 281.

Page 4: 5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study

(24.) Square Root **

Definition: For any real numbers a and b, if

then a is a square root of b or

We can also write square roots using the ½ power.

ba 2

bb 2

Page 5: 5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study

(25.) Cube Root **

Definition: For any real numbers a and b, if

then a is a cube root of b or

We can also write cube roots using the 1/3 power.

ba 3

ab 3

Page 6: 5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study

(26.) nth Root **

Definition: For any real numbers a and b, if

then a is a nth root of b or

We can also write nth roots using the power.

ban abn

nn bb 1

Page 7: 5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study

(27.) Principal RootDefinition: When there is more than one real

root of a number, the non-negative root is the principal root

Principal Root

Negative Root

Both864

864

Page 8: 5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study

Evaluating Roots of Monomials

To find a root of a monomial, split the monomial into a product of the factors, and evaluate the root of each factor.

Examples:

325 155 1055 1510

488

23232

74949

yxyxyx

xxx

Page 9: 5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study

Even Roots

When evaluating even roots (n is even) use absolute values.

4 4

Page 10: 5-5 Roots of Real Numbers Objective: To simplify radicals having various indices, and to use a calculator to estimate the roots of numbers. HW: 5-5 Study

Roots of negative numbers

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