Simplifying Radicals with Variables

The video tutorial explains how to simplify radicals with non-perfect square radicands containing variables. It begins with the prime factorization of 96 to identify perfect square factors, then demonstrates simplifying the square root of 96x⁹y⁴. The tutorial continues with simplifying negative two times the cube root of 54x⁴, highlighting the importance of finding perfect cube factors. The video concludes by emphasizing the usefulness of prime factorization in simplifying radicals.

What is the first step in simplifying radicals that are not perfect squares?

• Identify the radicand

• Simplify the expression directly

• Perform prime factorization

• Group the factors

What is the prime factorization of 96 in the context of simplifying radicals?

• 2x2x2x2x2x3

• 2x3x16

• 8x12

• 4x24

How is x^9 written to identify groups of two equal factors?

• x^2 x^2 x^2 x^2 x

• x^3 x^3 x^3

• x^4 x^4 x

• x^2 x^2 x^2 x^2 x^2

What is the simplified form of the square root of 96x^9y^4?

• 2x^5y^2√3

• 8x^3y√12x

• 4x^2y√24x

• 4x^4y^2√6x

What remains under the radical after simplifying the square root of 96x^9y^4?

• 3x

• 12x

• 24x

• 6x

What is the prime factorization of 54 in the context of simplifying cube roots?

• 3x3x2x3

• 9x6

• 2x27

• 18x3

How is x^4 written to identify groups of three equal factors for cube roots?

• x^4

• x^3 x

• x^2 x^2

• x x x x

What is the simplified form of the cube root of 54x^4?

• -3x∛18x

• -9x∛6x

• -6x∛2x

• -6x^2∛3x

What remains under the cube root after simplifying 54x^4?

• 2x

• 3x

• 6x

• 9x

Why is prime factorization useful in simplifying radicals?

• It helps identify perfect square and cube factors.

• It simplifies numerical calculations.

• It reduces the number of variables.

• It eliminates the need for radicals.