Simplifying Radicals and Roots

The video tutorial explains how to subtract radical expressions by ensuring they are like radicals, meaning they have the same index and radicand. It demonstrates simplifying square and cube roots using prime factorization to identify perfect square and cube factors. The tutorial provides examples of simplifying and subtracting radicals, emphasizing the importance of treating radicals like variables when they are similar.

What must be true for two radicals to be considered 'like radicals'?

• They must be both cube roots.

• They must be both square roots.

• They must have the same index and radicand.

• They must have the same coefficient.

What is the first step in simplifying the square root of a number?

• Divide by the index.

• Identify perfect square factors.

• Add the coefficients.

• Multiply the radicands.

How is the square root of 12 simplified using prime factorization?

• As 4 * 3

• As 2 * 3

• As 2^2 * 3

• As 3^2 * 2

What is the result of subtracting 6√3 from 4√3?

• 0

• 10√3

• 2√3

• √3

What is the first step in simplifying the cube root of a number?

• Add the coefficients.

• Multiply the radicands.

• Identify perfect cube factors.

• Divide by the index.

How can x^4 be expressed to simplify the cube root?

• x^2 * x

• x^2 * x^2

• x^3 * x

• x^4

What is the simplified form of the cube root of x^3?

• 1

• x

• x^2

• x^3

What is the result of subtracting x * ∛(xy^2) from 2x * ∛(xy^2)?

• 3x * ∛(xy^2)

• x * ∛(xy^2)

• 2x * ∛(xy^2)

• 0

When simplifying radicals, when is an absolute value necessary?

• When the index is odd.

• When the index is even and the variable has an odd exponent.

• When the radicand is negative.

• When the coefficient is negative.

What is the simplified form of the expression 2 * ∛(x^4y^2) - x * ∛(xy^2)?

• 2x * ∛(xy^2)

• 0

• x * ∛(xy^2)

• 3x * ∛(xy^2)