Square Roots and Prime Factorization

The video tutorial explains how to simplify square roots of non-perfect squares by identifying perfect square factors within the radicand. It demonstrates this process through several examples, including the square roots of 45, 8, 48, 150, and 1350. The tutorial emphasizes the use of prime factorization and the product rule for square roots to achieve simplification.

What is a necessary condition for a square root to simplify?

• The radicand must be a prime number.

• The radicand must contain perfect square factors.

• The radicand must be a negative number.

• The radicand must be an even number.

What is the simplified form of the square root of 45?

• 3 square root 5

• 5 square root 3

• 9 square root 5

• 15 square root 3

What is the product rule for square roots?

• The square root of a sum is the sum of the square roots.

• The square root of a difference is the difference of the square roots.

• The square root of a product is the product of the square roots.

• The square root of a quotient is the quotient of the square roots.

Which of the following is a perfect square factor of 8?

• 6

• 8

• 4

• 2

How can the square root of 48 be simplified using its prime factors?

• 8 square root 1

• 2 square root 12

• 4 square root 3

• 6 square root 2

What is the prime factorization of 48?

• 3 x 3 x 3 x 2

• 4 x 4 x 3

• 2 x 3 x 4 x 4

• 2 x 2 x 2 x 2 x 3

What is the prime factorization of 150?

• 3 x 3 x 5 x 5

• 2 x 3 x 5 x 5

• 2 x 5 x 15

• 3 x 5 x 10

What is the simplified form of the square root of 150?

• 15 square root 2

• 5 square root 6

• 20 square root 1

• 10 square root 3

Which of the following is a perfect square factor of 1350?

• 3 x 3

• 2 x 2

• 4 x 4

• 5 x 5

What is the simplified form of the square root of 1350?

• 10 square root 15

• 12 square root 10

• 18 square root 5

• 15 square root 6