Prime Factorization and Radical Simplification

The video tutorial explains how to simplify radicals with non-perfect square radicands and variables. It begins with the prime factorization of 96 to identify perfect square factors, then demonstrates simplifying the square root of 96x⁹y⁴. The process involves grouping factors to find perfect squares and simplifying the expression. The tutorial then shifts to simplifying the cube root of -2 times 54x⁴, using a similar method to find perfect cube factors. The video concludes by highlighting the usefulness of prime factorization in simplifying radicals.

What is the first step in simplifying radicals with non-perfect square radicands?

• Multiply the coefficients

• Identify the variables

• Circle the radicand

• Find the prime factorization

What is the prime factorization of 96?

• 2 x 48

• 2^5 x 3

• 3 x 32

• 4 x 24

How do you express x to the ninth power for simplification?

• x^2 x^2 x^2 x

• x^3 x^3 x^3

• x^4 x^4 x

• x^5 x^4

Which of the following is a perfect square factor?

• x^2

• y

• x^3

• y^3

What is the simplified form of the expression 4x^4y^2√6x?

• 4x^3y^2√6x

• 4x^5y^2√6x

• 4x^4y^2√6x

• 4x^4y^3√6x

What is the first step in simplifying cube roots?

• Identify the cube root

• Find the prime factorization

• Circle the radicand

• Multiply the coefficients

What is the prime factorization of 54?

• 6 x 9

• 3^3 x 2

• 2 x 27

• 4 x 13.5

How do you express x to the fourth power for cube root simplification?

• x^3 x^2

• x^3 x

• x^2 x^2

• x^4

What is the simplified form of the expression -6x^3∛2x?

• -6x^4∛2x

• -6x^3∛2x

• -6x^3∛3x

• -6x^2∛2x

Why is prime factorization helpful in simplifying radicals?

• It reduces the number of variables

• It simplifies addition

• It helps identify perfect square and cube factors

• It makes multiplication easier