Understanding Square Roots and Like Radicals

The video tutorial explains how to simplify square roots by identifying perfect square factors through prime factorization. It demonstrates the process using examples of square roots of 28, 63, 48, and 75, showing how to simplify them to like radicals and then add them. The tutorial emphasizes the importance of recognizing perfect square factors to simplify expressions effectively.

What is the first step in simplifying square roots?

• Multiply the square roots

• Identify perfect square factors

• Find the sum of the square roots

• Identify like radicals

What is the prime factorization of 28?

• 2 x 2 x 7

• 3 x 3 x 7

• 5 x 5 x 3

• 4 x 7

Which of the following is a perfect square factor of 63?

• 3 x 3

• 2 x 2

• 7 x 7

• 5 x 5

How do you combine like radicals?

• By subtracting them

• By multiplying them

• By adding them like terms

• By dividing them

What is the sum of 2√7 and 3√7?

• 7√7

• 8√7

• 6√7

• 5√7

What is the prime factorization of 48?

• 4 x 4 x 3

• 3 x 3 x 3 x 2

• 2 x 2 x 2 x 2 x 3

• 5 x 5 x 2

Which of the following is a perfect square factor of 75?

• 2 x 2

• 3 x 3

• 7 x 7

• 5 x 5

What is the simplified form of 4√3 + 5√3?

• 11√3

• 10√3

• 9√3

• 8√3

What is the result of simplifying the square root of 48?

• 7√3

• 4√3

• 5√3

• 6√3

What is the sum of the square roots of 48 and 75?

• 11√3

• 8√3

• 10√3

• 9√3