Geometry/Trig Name: __________________________________

Date: ___________________________________

Lesson 4-1: Radicals

Learning Goals: (1) How do we calculate perimeter of familiar polygons? (2) How do we simplify radical expressions?

Simplifying Radicals

1st: Watch Me Simplify:

1. √18 2. 2 √216

2nd: Partner Work

Using the steps and guided example below, simplify the following radical: √72

Note! When we say

“radical” it means

“square root”!

Geometry/Trig Quick Summary:

1. When you find a pair of numbers under the radical, how many go in front of the radical symbol?

2. What do you do with all of the numbers on the outside/in front of the radical symbol? What about the inside?

*Example:

3rd: You try on your own!

Put the following in simplest radical form: 𝟑√𝟑𝟐.

Use the steps we just looked at to help guide you!

Think-Pair-Share in your Group:

Is the following equation true or false? How can you check?

√ 5 + √5 = √10

Geometry/Trig

Radical Operations

ADDING RADICALS

Look at the following equations. What do you notice about the numbers under the radical in the original

problem and the final answer?

Example 1) Example 2)

585652 242723

You try: 2623 = ________________

Operation Helpful Hints Examples

Addition For these you must have “like terms”. That

means the number under the radicals must

be the same in order to combine them. If

they aren’t the same, try simplifying!

Example

5√7 + 13√7 =18√7

Subtraction

Non-Example

2√3 - √5 =2√3 - √5

(Can’t be simplified any farther)

Together! On Your Own!

5√8 + 3√18 √24 + √54

Geometry/Trig PRACTICE

6 - 6 8 + 18

3 3 + 4 3 - 2 8 7 12 7

5 + 2 5 + 3 5

5 36 + 4 30

4 12 - 75

3 6 5 24

2√36 + √4 √16 + √54

Geometry/Trig Name: _________________________________

Date: _________________________

Lesson 1-1: Homework

Directions: Simplify the following expressions. Express each answer in

simplest radical form.

1. Simplify the following:

a) √50 b) √𝑥3

c) 4√27 d) √18𝑦2

e) 4 5 5 f) 10 11 24 11

Geometry/Trig

g) 2 15 7 15 h) 20 3 4 27

i)17 8 5 44 j) −9√15 + 10√15

k) −2√3 + 3√27

l) −3√5 − 2√24 − 3√5