Prime Factorization and Roots

This video tutorial teaches how to convert entire radicals into mixed radicals. It covers three examples: the square root of 80, the cubed root of 144, and the fourth root of 162. Each example involves identifying prime factors and grouping them into pairs, triplets, or quadruplets, depending on the root. The video concludes with a call to action for viewers to engage with the channel.

What is the first step in converting an entire radical to a mixed radical?

• Find the square root directly.

• Write out the prime factors.

• Multiply the numbers.

• Divide by 2.

Which of the following is a prime factor of 80?

• 3

• 5

• 7

• 9

What should you do if you don't know how to find prime factors?

• Watch a tutorial video.

• Skip the step.

• Guess the factors.

• Use a calculator.

How many pairs of 2s are there in the prime factorization of 80?

• 1

• 4

• 2

• 3

What is the simplified form of the square root of 80?

• 4√5

• 8√5

• 16√5

• 2√5

What is the cube root of 144 expressed in terms of its prime factors?

• 2 * 2 * 2 * 3 * 3

• 2 * 2 * 3 * 3

• 2 * 3 * 3

• 2 * 2 * 2 * 2 * 3

How many triplets can be formed from the prime factors of 144?

• 1

• 2

• 3

• 4

What is the simplified form of the cube root of 144?

• 3 * ³√18

• 2 * ³√18

• 2 * √18

• 4 * ³√18

What is the fourth root of 162 expressed in terms of its prime factors?

• 2 * 2 * 3 * 3

• 3 * 3 * 3

• 2 * 2 * 2 * 2

• 3 * 3 * 3 * 3

How many quadruplets can be formed from the prime factors of 162?

• 1

• 2

• 3

• 4