Simplifying Radicals and Factor Trees

The video tutorial explains how to simplify square roots using the factor tree method. It begins by introducing the method and then demonstrates how to create a factor tree for the number 108. The process involves breaking down 108 into its prime factors and then using these factors to simplify the square root. The tutorial emphasizes the importance of identifying pairs of prime numbers to simplify the radical expression effectively.

What method is introduced for simplifying square roots?

• Division method

• Radical pairing

• Factor tree method

• Prime factorization

What is the first step in using the factor tree method?

• Draw branches

• List all factors

• Divide the number by 2

• Identify even numbers

Which number is used as an example to simplify using the factor tree method?

• 9

• 108

• 27

• 54

What is the result of factoring 54 in the factor tree?

• 5 and 10

• 3 and 18

• 2 and 27

• 6 and 9

How is the number 9 further broken down in the factor tree?

• 1 times 9

• 2 times 4.5

• 3 times 3

• 4.5 times 2

What does the rewritten form of 108 consist of?

• Multiples of 2 and 3

• Multiples of 4 and 5

• Multiples of 6 and 7

• Multiples of 8 and 9

What happens to paired numbers under the radical sign?

• They are moved outside the radical

• They are squared

• They are multiplied

• They are subtracted

What remains inside the radical after pairing?

• All composite numbers

• Unpaired numbers

• All prime numbers

• Paired numbers

What is the simplified form of the square root of 108?

• 9 square root of 2

• 6 square root of 3

• 3 square root of 6

• 12 square root of 3

What mathematical process is used to simplify the square root of 108?

• Multiplication

• Addition

• Subtraction

• Factorization