Properties of Radicals - Day 2: Pugh

Properties of Radicals Day II

​Ms. Pugh - Algebra 1

Match

Do Now: Match the following. (20 Points)

• radical expression

• simplest form of a radical

  (no radicals in the denominator of a fraction)

• rationalizing the denominator

an expression that contains a radical

NO RADICANDS

1. have perfect nth powers as factors other than 1.

2. contain fractions.

eliminating the radical from the denominator (multiplying by a form of "1")

conjugates

• an expression that contains a radical

• NO RADICANDS

  1. have perfect nth powers as factors other than 1.

  2. contain fractions.

• eliminating the radical from the denominator (multiplying by a form of "1")

• conjugates

Reorder

Learning Target: Reorder the following. (10 points)

• I can

• use properties

• of radicals

• to write

• equivalent expressions.

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Open Ended

Focus Question: How can we write a cube root in simplest form? (10 points)

Open Ended

Summarize. (20 points).

Multiple Select

Check For Understanding (10 points)

Identify the radical expression (s) that are in simplest form. (select all)

Open Ended

Summarize. (20 points).

Multiple Choice

Check For Understanding (10 points)

$$\sqrt[]{108}$$

Hint: Find the greatest square factor.

• $$6\sqrt[]{3}$$

• 10

• $$\sqrt[]{36\times3}$$

• 54

Math Response

Check For Understanding (10 points)

$$\sqrt[]{9x^3}$$

Hint: Find the greatest square factor.

Type answer here

Correct Answer: 3x\sqrt{x}

Deg^°

Rad

Open Ended

Summarize. (20 points).

Multiple Choice

Check For Understanding (10 points)

$$\sqrt[]{\frac{81}{x^2}}$$

• $$\frac{9}{x}$$

• 9x

• $$9x^2$$

• $$\frac{\sqrt[]{81}}{x^2}$$

Math Response

Check For Understanding (10 points)

$$\sqrt[]{\frac{15}{64}}$$

Type answer here

Correct Answer: \frac{\sqrt{15}}{8}

Deg^°

Rad

Multiple Choice

Guided Practice: (10 points)

Simplify the expression.

• $$5\sqrt[]{5b}$$

• $$\sqrt[]{25\times5b}$$

• 25b

• $$\sqrt[]{25b}$$

Math Response

Guided Practice: (10 points)

Simplify the expression.

- $$\sqrt[]{81x^3}$$

Type answer here

Correct Answer: -9x\sqrt{x}

Deg^°

Rad

Draw

Self- Assessment

Multiple Choice

Independent Practice: (15 points)

Simplify

√128

• 64√2

• 16

• 2√8

• 8√2

Multiple Choice

Independent Practice: (15 points)

Simplify

√200

• 14

• 20√8

• 5√3

• 10√2

Multiple Choice

Independent Practice: (15 points)

Simplify √45n³

• 3n√5n

• 4n√8

• 4n√-8

• 10√n

Open Ended

Debrief (20 Points):

Did you reach the Learning Target?

Can you answer the Focus Question?

Open Ended

Exit Ticket: (20 points)

Error analysis: Describe and correct the error in writing $$\sqrt[]{72}$$ in simplest form.