Simplifying Square Roots and Factorization

The video tutorial explains how to simplify square roots by identifying perfect square factors through prime factorization. It demonstrates the process with examples of simplifying the square roots of 50 and 675, emphasizing the importance of recognizing perfect square factors and focusing on principal square roots.

What is a perfect square factor?

• A number that can be divided by 2

• A number that is a product of two equal factors

• A number that is a prime number

• A number that is a multiple of 10

What is the prime factorization of 50?

• 2 * 5 * 5

• 5 * 5 * 5

• 3 * 5 * 5

• 2 * 2 * 5

How can the square root of 50 be simplified?

• 10 * √5

• 2 * √5

• 5 * √2

• 5 * √5

What is the first step in finding the prime factorization of 675?

• Divide by 2

• Divide by 3

• Divide by 5

• Divide by 7

Which of the following is a perfect square factor in the prime factorization of 675?

• 3 * 3

• 5 * 5

• 3 * 5

• Both 3 * 3 and 5 * 5

What is the prime factorization of 675?

• 3 * 3 * 3 * 5 * 5

• 2 * 3 * 5 * 5

• 3 * 5 * 5 * 5

• 2 * 2 * 3 * 5

How can the square root of 675 be simplified?

• 15 * √3

• 25 * √3

• 10 * √3

• 5 * √3

What is the result of simplifying the square root of 3 * 3?

• 9

• 1

• 5

• 3

What is the result of simplifying the square root of 5 * 5?

• 1

• 10

• 3

• 5

What remains under the square root after simplifying the square root of 675?

• √2

• √3

• √5

• √10