Understanding Fourth Roots

The video tutorial explains how to find the fourth root of numbers using factorization. It starts with the example of 81, breaking it down into its prime factors to find the fourth root. The process is repeated for 512, using a calculator to assist with larger numbers. The tutorial demonstrates grouping factors to simplify the expression and find the fourth root, emphasizing the importance of understanding factor trees and prime factorization.

What is the fourth root of 81?

• 2

• 9

• 3

• 4

How many factors of 3 are needed to find the fourth root of 81?

• 4

• 3

• 5

• 2

What is the first step in finding the fourth root of 512?

• Multiply by 2

• Divide by 2

• Multiply by 3

• Divide by 3

After dividing 512 by 2, what is the next number obtained?

• 128

• 256

• 64

• 32

What is the result of dividing 256 by 2?

• 32

• 128

• 16

• 64

How many times do you divide by 2 to reach 64 from 512?

• 2

• 3

• 5

• 4

How many groups of four are formed from the factors of 512?

• 4

• 1

• 3

• 2

What remains inside the radical after grouping the factors of 512?

• Three 2s

• Two 2s

• Four 2s

• One 2

What is the simplified form of the fourth root of 512?

• 32√2

• 16√2

• 8√2

• 4√2

What is the final coefficient outside the radical for the fourth root of 512?

• 2

• 4

• 8

• 6