Simplifying Square Roots: Key Concepts and Techniques

The video tutorial explains how to simplify square roots using a factor tree method. It begins by introducing the concept of square roots and the need for simplification when the result is not a simple number. The tutorial then demonstrates how to create a factor tree, breaking down numbers into their prime factors. It explains the process of pairing primes and removing them from the square root, using examples like the square roots of 72 and 120. The video provides a clear, step-by-step guide to simplifying square roots, making it easier for students to understand and apply the method.

What is the square root of 4?

• 3

• 2

• 4

• 1

What is the square root of 100?

• 10

• 20

• 5

• 15

What is the first step in simplifying a square root like √72?

• Multiply the number by itself

• Add the digits of the number

• Create a factor tree

• Divide the number by 2

What is the purpose of creating a factor tree?

• To add the factors

• To multiply the factors

• To break down the number into prime factors

• To find the sum of the factors

When simplifying √72, which pairs of primes are identified?

• Pairs of 2s and 5s

• Pairs of 3s and 5s

• Pairs of 2s and 3s

• Pairs of 3s and 7s

What do you do with pairs of primes when simplifying a square root?

• Add them together

• Multiply them together

• Leave them inside the square root

• Take one of each pair out of the square root

What is the simplified form of √72?

• 6√2

• 12√3

• 12√2

• 6√3

What is the first step in simplifying √120?

• Divide by 2

• Create a factor tree

• Multiply by 10

• Add the digits

Which pair of primes is identified when simplifying √120?

• Pairs of 7s

• Pairs of 5s

• Pairs of 3s

• Pairs of 2s

What is the simplified form of √120?

• 2√15

• 2√30

• 10√2

• 10√3