Simplifying Radicals with Coefficients

The video tutorial covers the process of simplifying radicals, starting with an introduction to the concept and moving through several examples. The teacher explains how to factor numbers using prime factorization, identify pairs of factors, and simplify the expression by moving pairs outside the radical. Each example demonstrates these steps in detail, ensuring students understand the process. The video concludes with a summary of the steps involved in simplifying radicals.

What does the coefficient in front of a radical signify?

• It is multiplied by the radical.

• It is subtracted from the radical.

• It is added to the radical.

• It is divided by the radical.

What is the first step in simplifying 2√108?

• Multiplying the coefficient by 108.

• Prime factorization of 108.

• Dividing 108 by 2.

• Adding the numbers inside the radical.

After prime factorization, what do you do with pairs of numbers?

• Subtract them.

• Add them together.

• Move them outside the radical.

• Leave them inside the radical.

What is the simplified form of 2√108?

• 4√3

• 6√3

• 12√3

• 8√3

What is the prime factorization of 60?

• 5 × 12

• 3 × 20

• 2 × 2 × 3 × 5

• 2 × 30

What is the simplified form of 7√60?

• 28√15

• 7√15

• 21√15

• 14√15

What is the prime factorization of 125?

• 5 × 5 × 5

• 25 × 5

• 5 × 25

• 10 × 12.5

What is the simplified form of -10√125?

• -40√5

• -30√5

• -20√5

• -50√5

What is the prime factorization of 500?

• 5 × 100

• 2 × 250

• 10 × 50

• 5 × 5 × 20

What is the simplified form of 8√500?

• 60√5

• 20√5

• 80√5

• 40√5