Roots of Real Numbers lesson 5-5 Learning Targets: I can simplify radicals. I can use a calculator to approximate radicals.

Simplifying Radicals Even Roots: Odd Roots:       index power             power index                   If you have an even root and an odd powered answer, you must take the absolute value of it to get the principal root.    

Example 1: Simplify. a.     or           b.       c.

Your Turn 1: Simplify. a. b. c.

Example 2: Simplify. a. b.

Your Turn 2: Simplify. a. b. c.

Example 3: Use a calculator to approximate each value to three decimal places. a.   Look at the Math button on the calculator:   b.       c.

Your Turn 2: Use a calculator to approximate each value to three decimal places. a.   b.   c.  

Learning Targets Reflection: I can simplify radicals. I can use a calculator to approximate radicals.

Divide using synthetic division 3. Warm- up Day # 8 Alg. 2B Simplify. a) b) c) Factor. a) b) Divide using synthetic division 3.

Radical Expressions lesson 5-6 Objectives: Simplify radical expressions. Add, subtract, multiply, and divide radical expressions.

Example 1: Simplify. a. b.

Your Turn 1: Simplify. a. b. c.

Example 2: Simplify. a. b.

Your Turn 2: Simplify. a. b.

Example 3: Simplify. (Adding radicals.)

Your Turn 3: Simplify.

Example 4: Simplify. (Multiplying radicals.) b.

Your Turn 4: Simplify. a.

b.

Example 5: Simplify. (Dividing radicals.) Remember conjugates!!! a.

b.

Your Turn 5: Simplify. a.

b.

Lesson 5-6: RADICAL EXPRESSIONS CFU: pg. 256, Practice Quiz 2 (all) Practice 5.6 (worksheet)

Simplify the following. 1. Warm- up Day # 9 Alg. 2B Simplify the following. 1. 2. Factor the following. 3. 4.

Rational Expressions lesson 5-7 Objectives: Write expressions with rational exponents in radical form, and vice versa. Simplify expressions in exponential or radical form.

Example 1: Example 2:

Example 3:

Example 1: Write the expression in radical form. Your Turn 1: Write the expression in radical form.

Example 2: Write each radical using rational exponents. b.

Your Turn 2: Write each radical using rational exponents. b.

Example 3: Simplify. a.

b.

c.

Your Turn 3: Simplify. a. b. c.

Radical Equations lesson 5-8 Learning Target: I can solve equations containing radicals.

Solve Radical Equations: The following steps are used in solving equations that have variables in the radicand. Some algebraic procedures may be needed before you use these steps. Step 1: Isolate the radical on one side of the equation. (No #’s in front or separate.) Step 2: To eliminate the radical, raise each side of the equation to a power equal to the index of the radical. Step 3: Solve the resulting equation. Step 4: Check your solution in the original equation to make sure that you have not obtained any extra roots.

Example 1: Solve. Check:

Your Turn 1: Solve. Check:

Example 2: Solve. Check:

Your Turn 2: Solve. Check:

Your Turn 3: Solve and check each equation.

Your Turn 3: Solve and check each equation. b.

Your Turn 3: Solve and check each equation.

Complex Numbers lesson 5-9 Learning Targets: I can add and subtract complex numbers. I can multiply and divide complex numbers.

Imaginery:

Example 1: Simplify. (add & subtract)

Your Turn 1: Simplify. a. b. c.

Example 2: Simplify. (multiply)

Your Turn 2: Simplify.

Example 3: Simplify. (divide)

Your Turn 3: Simplify.

Example 4: Solve.

Your Turn 4: Solve.

Check for understanding. Simplify. 1. 2.

Check for understanding. 3. 4. Solve. 4.