Prime Factorization and Simplifying Radicals

The video tutorial explains how to simplify radicals and cube roots when the radicand is not a perfect square and contains variables. It begins with the prime factorization of numbers to identify perfect square and cube factors. The process involves rewriting expressions to group equal factors, simplifying them by taking one factor from each group, and leaving non-grouped factors under the radical. The tutorial covers both square roots and cube roots, demonstrating the method with examples.

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

• Identify the variables

• Find the prime factorization

• Multiply the coefficients

• Circle the radicand

What is the prime factorization of 96?

• 2 * 48

• 4 * 24

• 3 * 32

• 2^5 * 3

How do you identify perfect square factors in an expression?

• By subtracting the exponents

• By adding the coefficients

• By circling groups of two equal factors

• By dividing by 2

What do you do with the circled perfect square factors?

• Multiply them together

• Divide them by the radicand

• Take one factor from each group

• Add them to the radicand

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

• 2x^2y√6x

• 4x^4y^2√6x

• 8x^3y^2√3x

• 6x^2y√2x

What is the first step in simplifying a cube root?

• Identify the variables

• Find the prime factorization

• Circle the radicand

• Multiply the coefficients

What is the prime factorization of 54?

• 6 * 9

• 3^2 * 2

• 3^3 * 2

• 2 * 27

How do you identify perfect cube factors in an expression?

• By adding the coefficients

• By circling groups of three equal factors

• By dividing by 3

• By subtracting the exponents

What do you do with the circled perfect cube factors?

• Take one factor from each group

• Divide them by the radicand

• Multiply them together

• Add them to the radicand

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

• -2x∛3x

• -4x∛3x

• -6x∛2x

• -3x∛6x