Simplifying Radicals Using Factor Trees

Simplifying Radicals Using Factor Trees

by Terrie Dabit

Poll

Did you know that radicals need to be simplified? For example what about  $$\sqrt[]{75}$$  ?

Multiple Choice

Which of these areas is a perfect square?

• 12
• 90
• 40
• 64

Multiple Choice

Which of the following in NOT a perfect square?

• 49

• 81

• 111

• 144

Open Ended

Explain the difference in PRIME and COMPOSITE numbers. If you don't know, go Google it and write a definition in your own words. Give an example of each.

​Simplifying radicals involves knowing PERFECT SQUARES & PRIME NUMBERS

​Watch this NEW way to reduce radicals that involves using FACTOR TREES.

Multiple Choice

$$\sqrt{50}$$  

• $$5\sqrt{2}$$  

• $$\sqrt{5}$$   

• $$2\sqrt{5}$$  

• $$25\sqrt{2}$$  

Multiple Choice

$$\sqrt{96}$$

• $$16\sqrt{6}$$  

• $$2\sqrt{6}$$  

• $$4\sqrt{6}$$  

• $$\sqrt{2}$$  

Multiple Choice

$$\sqrt{63}$$  

• $$9\sqrt{7}$$  

• $$6\sqrt{2}$$  

• $$7\sqrt{6}$$  

• $$3\sqrt{7}$$  

Multiple Choice

Simplify 4√75

• 4√5
• 12√5
• 20√3
• 7√3

Multiple Choice

4√8

• 16
• 8√2
• 4√2
• 2√4

Multiple Choice

Simplify:  √31

• 3√1
• already simplified
• 1√3
• 15√2 + 1

Multiple Choice

√1 =

• 1

• 2

• 0

• 1/2

​What do I do when there are variables to simplify?

​Watch this video to see how you can pull variables with EVEN exponents to the outside. Those leftover variables to the first power can just be left under the radical sign.

Multiple Choice

Simplify the radical...
√20a²b⁴

• 2ab²√5
• 4ab²√5
• 5ab²√2
• 2a²b²√5

Multiple Choice

Simplify

√45n³

• 3n√5n
• 4n√8
• 4n√-8
• 10√n

Multiple Choice

√36x³y⁴

• 6y²x√x
• 3y²√2x
• 3y√x
• 6x√3y

Multiple Choice

√28m⁴n³

• m²n√7n
• 7m²n√n
• 2m²n√7n
• 7m²n²√n

Multiple Choice

$$12\sqrt{48x^5y^7z}$$  

• $$48x^2y^3\sqrt{3x}$$  

• $$16x^2y^3\sqrt{3xz}$$  
  

• $$72x^2y^2\sqrt{8x^2y^4z}$$  

• None of the above

Poll

I feel confident that I can simplify my radicals.