U5-S1-L1 Simplifying Radicals

1
U5-S1-L1 Simplifying Radicals

• Essential Question
• How do you simplify radicals involving products
  and quotients?

2
Main Idea Vocabulary

• Our goal in this lesson will be to simplify
  radical expressions.
• An expression that contains a radical sign (
  ) is a radical expression.
• The expression under a radical sign is the
  radicand.
• A radicand may contain numbers, variables, or
  both.
• It may contain one or more terms.

3
Simplifying Radical Expressions

• A radical expression is in simplest form if
• the radicand has no perfect squares
• the radicand has no fractions
• No square roots in the denominator
• Remember, taking the square root means there can
  be positive or negative roots.
• Because of this, we may need to include absolute
  values in our answers.

4
Ex 1- Simplifying Radical Expressions

• To simplify, use any skills to break it down.

5
Practice 1
6
Product Property of Square Roots

• Product Property of Square Roots For positive
  real numbers, vab vavb

7
Ex 2-Using Product Property ofSquare Roots

1. Break down numbers to take out perfect squares
2. Break down exponents by making them even numbers
3. Divide even exponents by 2 and leave odd
   exponents inside radical

8
Practice 2
9
Ex 1 Multiplying Square Roots

• Multiply terms together under radical
• Multiply terms together outside the radical
• Simplify

10
Practice
11
Quotient Property of Square Roots

• Quotient Property of Square Roots For positive
  real numbers,

12
Ex 3- Using Quotient Property

1. Simplify the numerator
2. Simplify the denominator

13
Practice 3
14
Ex 4-Using Product Quotient Properties Together
15
Practice 4
16
Ex 4-Rationalizing the Denominator

• You CANT have square roots in the DENOMINATOR,
  so you must get rid of them. This is called
  rationalizing the denominator.
• To rationalize the denominator, multiply both top
  and bottom by it.

17
Ex 4-Rationalizing the Denominator
18
Practice 4
19
Summary

• Answer the essential question in detailed,
  complete sentences.
• How do you simplify radicals involving products
  and quotients?
• Write 3-5 study questions in the left column to
  correspond with the notes.