Prime Factorization and Verification

The video tutorial explains how to rewrite radicals by factoring out the radicands using their prime factorization. It begins with an introduction to the concept of radicals and the importance of prime factorization. The tutorial then provides step-by-step examples of finding the prime factorization for the square root of 16, the square root of 80, and the cube root of 312, demonstrating how to verify the calculations.

What is the purpose of rewriting radicals using prime factorization?

• To make the numbers larger

• To simplify calculations

• To change the radical sign

• To increase the index of the radical

What is the prime factorization of 16?

• 8 * 2

• 4 * 4

• 2 * 2 * 2 * 2

• 2 * 2 * 2

How can you verify the prime factorization of 16?

• By subtracting the factors

• By dividing the factors

• By multiplying the factors

• By adding the factors

What is the prime factorization of 80?

• 2 * 2 * 2 * 5

• 2 * 2 * 2 * 2 * 5

• 4 * 4 * 5

• 8 * 10

Which of the following is NOT a prime factor of 80?

• None of the above

• 5

• 2

• 10

What is the prime factorization of 312?

• 2 * 2 * 2 * 3 * 13

• 2 * 2 * 3 * 13

• 3 * 13

• 2 * 3 * 13

How do you verify the prime factorization of 312?

• By subtracting the factors

• By adding the factors

• By multiplying the factors

• By dividing the factors

Which of the following is a prime factor of 312?

• 26

• 13

• 6

• 4