Prime Factorization and Verification

The video tutorial explains how to rewrite radicals by factoring the radicands into their prime factors. It begins with an introduction to the concept, followed by examples using the square root of 16 and 80, and concludes with the cube root of 312. Each example demonstrates the process of breaking down numbers into their prime factors to simplify the radicals.

Why is it helpful to rewrite radicands using their prime factorization?

• It makes the calculation more complex.

• It changes the value of the radicand.

• It simplifies the process of finding roots.

• It makes the numbers larger.

What is the prime factorization of 16?

• 8 x 2

• 4 x 4

• 2 x 2 x 2 x 2

• 2 x 2 x 2

How can you verify the prime factorization of 16?

• By adding the factors.

• By dividing the factors.

• By subtracting the factors.

• By multiplying the factors.

What is the prime factorization of 80?

• 4 x 4 x 5

• 2 x 2 x 2 x 2 x 5

• 2 x 2 x 2 x 5

• 8 x 10

Which of the following is a correct step in verifying the prime factorization of 80?

• 2 x 2 = 4

• 2 x 5 = 10

• 2 x 2 = 5

• 5 x 5 = 25

What is the prime factorization of 312?

• 2 x 2 x 2 x 3 x 13

• 2 x 2 x 3 x 13

• 2 x 3 x 13

• 3 x 13

How do you verify the prime factorization of 312?

• By adding the factors.

• By dividing the factors.

• By multiplying the factors.

• By subtracting the factors.

What is the result of multiplying 24 by 13?

• 312

• 300

• 320

• 330