Unit 1 Relationships Between Quantities and Expressions

Week 2

Lesson 1 – Simplify Radicals

(restricted to square roots only)

Today’s Objective • MGSE9-12.N.RN.2 Rewrite expressions involving

radicals (restricted to square roots only)

• MGSE9-12.N.RN.3 Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.

• Objective: Students will simplify radical expressions

Essential Questions

• What do you already know about square roots?

• What is a perfect square?

• What is rational number?

• What is a irrational number?

Vocabulary

• Simplify

• Like Terms

• Radicals

• Radicands

• Simplest Form

• Factors

• Rational Numbers

• Irrational Numbers

Read, Write, Draw, Solve

Isaiah says that is an irrational number because it is a radical number. Do you agree or disagree, explain why.

Perfect Squares

The square of whole

numbers.

1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 ,

121, 144 , 169 , 196 , 225, etc

Square Root Of A Number

Recall: If b2 = a, then b is a square root of a.

Example: If 42

= 16, then 4 is a square root

of 16

What is a square root of 25? 64? 100?

5 8 10

Positive Square Root

Negative Square Root Positive & Negative Square Root

Is there a difference between

Which expression has no real

roots?

& ?

is not real

Evaluate the expression

The expression equal to is equivalent

to a positive integer when b is

A. -10

B. 64

C. 16

D. 4

You know how to find the square root

of a perfect square.

What happens if the number is not a

perfect square?

Does it have a square root?

What would the square root look like?

Numbers with a Root

Radical numbers are typically irrational numbers

(unless they simplify to a rational number). Our

calculator gives:

But the decimal will go on forever and not repeat because it is an irrational number. For the exact answer just use:

1.41421

2

2

Some radicals can be simplified similar to simplifying a fraction.

Rational/Irrational Numbers

• Review Game

• Practice with Rational/Irrational Numbers

What happens when the radicand is not a

perfect square?

Rewrite the radicand as a product of its

largest perfect square factor.

Simplify the square root of the perfect

square.

When simplified form still contains a

radical, it is said to be irrational.

Try These.

Identifying the largest perfect square factor when simplifying radicals

will result in the least amount of work.

Ex:

Not simplified! Keep going!

Finding the largest perfect square factor results in less work:

Note that the answers are the same for both solution processes

already in simplified form

A

B

D

C

Simplify

already in simplified form

A

B

D

C

Simplify

already in simplified form

A

B

D

C

Simplify

Simplify

already in simplified form

A

B

D

C

Simplify

already in simplified form

A

B

D

C

Note - If a radical begins with a coefficient before

the radicand is simplified, any perfect square that

is simplified will be multiplied by the existing

coefficient. (multiply the outside)

Express in simplest radical form.

Simplify

A

B

D

C

A

B

D

C

Simplify

A

B

D

C

Simplify

A

B

D

C

Simplify

A

B

D

C

Simplify

20

10

7

4

From the New York State Education Department. Office of Assessment Policy, Development and

Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

A

B

D

C

From the New York State Education Department. Office of Assessment Policy, Development and

Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

6

2

3

8

A

B

D

C

Exit Ticket

Online Practice

• Click on the link below and complete the practice

– For the True/False questions (1-3) you must provide an explanation for your choice.

– For problems 1-8 you must show work

• Practice Simplifying Radicals