Simplifying Radicals and Prime Factorization

The video tutorial explains how to simplify radicals by using prime factorization. It covers the simplification of square roots and cube roots, demonstrating the process with examples of the square root of 36, the square root of 12, and the cube root of 125. The tutorial emphasizes identifying squares and cubes within the prime factorization to simplify the radicals and multiply them by any existing coefficients.

What is the first step in simplifying a radical expression?

• Divide the numbers inside the radical.

• Multiply the numbers inside the radical.

• Find the prime factorization of the radicand.

• Add all the numbers inside the radical.

What is the prime factorization of 36?

• 3 * 3 * 4

• 2 * 2 * 3 * 3

• 2 * 3 * 3

• 2 * 3 * 6

After finding the prime factorization of 36, what is the next step in simplifying the square root?

• Identify and pull out pairs of factors.

• Add the factors together.

• Multiply the factors by 2.

• Divide the factors by 2.

What is the simplified form of the square root of 36?

• 4

• 7

• 5

• 6

What is the prime factorization of 12?

• 2 * 2 * 3

• 3 * 4

• 2 * 6

• 1 * 12

When simplifying 3√12, what remains inside the radical after simplification?

• 2

• 3

• 4

• 6

What is the prime factorization of 125?

• 2 * 2 * 31.25

• 10 * 12.5

• 5 * 25

• 5 * 5 * 5

What is the simplified form of 2 times the cube root of 125?

• 5

• 10

• 15

• 20

What is the purpose of simplifying radicals before adding or subtracting them?

• To change the operation to multiplication.

• To have like radical terms.

• To make the numbers larger.

• To eliminate the radicals completely.

What is the result of multiplying the coefficients after simplifying the cube root of 125?

• 10

• 5

• 15

• 20