Simplifying Square Roots and Factor Trees

The video tutorial explains how to simplify square roots using a factor tree method. It begins with an introduction to the concept and then provides several examples, including simplifying the square roots of 12, 124, 25, 72, and 125. Each example demonstrates the process of breaking down numbers into their prime factors, identifying pairs, and simplifying the expression under the square root sign. The video emphasizes the importance of recognizing prime numbers and pairs to simplify square roots effectively.

What is the first step in simplifying a square root using a factor tree?

• Divide the number by 2.

• Find the square of the number.

• Create a factor tree.

• Identify the largest factor.

When simplifying the square root of 12, what is the result after pulling out pairs?

• 2 square root 3

• 3 square root 2

• 6 square root 2

• 4 square root 3

In the example of simplifying the square root of 124, which prime numbers are identified?

• 7 and 31

• 5 and 62

• 3 and 41

• 2 and 31

What is the simplified form of the square root of 124?

• 4 square root 31

• 8 square root 31

• 2 square root 31

• 6 square root 31

What is unique about the number 25 in the context of simplifying square roots?

• It is an even number.

• It is a perfect square.

• It is a composite number.

• It is a prime number.

What is the simplified form of the square root of 25?

• 15

• 10

• 5

• 20

In the example of simplifying the square root of 72, which pairs are identified?

• 2 and 3

• 3 and 4

• 2 and 2

• 3 and 3

What is the simplified form of the square root of 72?

• 4 square root 2

• 5 square root 2

• 6 square root 2

• 7 square root 2

What is the first step in simplifying the square root of 125?

• Divide by 3

• Multiply by 2

• Subtract 5

• Create a factor tree

What is the simplified form of the square root of 125?

• 25 square root 5

• 15 square root 5

• 20 square root 5

• 10 square root 5