Radical Functions & Roots (Algebra 2 HN)

This is a Radical Functions and Roots review problem set. These questions are coming directly from an algebra 2 quiz, so use it wisely! I really hope this is useful!

Step 1: Simplify ∛(-54b³¹)

1) Factor -54

2) Factor b^31

3) Combine

Step 2: Simplify 5∛(4x²y³¹)×2∛(14x²)

1) Multiply terms inside and outside the radical

2) Factor x^4 & y^10

3) Factor 56

4) Combine

Step 3: Simplify ∜(64⁄9)

1) Multiply the denominator with the numerator

2) Factor 576

3) Combine

Step 4: Simplify ∛((56x⁴)⁄(7x))

1) Simplify inside the radical

2) Factor the cube root of 8x^3

3) Combine.

Step 5: Simplify ∜(75x²⁰y⁵z¹²)

1) Factor x^20.

*EEO Rule = 1) degree of radical is even

2) degree/exponent of variable is even

3) factor is odd

--> then include absolute value.

2) Factor y^5

3) Factor z^12

*EEO Rule

4) Combine

Step 6: Simplify -√m⁴²

1) Factor √m⁴²

2) Combine

Step 7: Simplify ∛(64x³y²)⁄∛(4xy⁷)

1) Simplify within radicals.

2) Factor the cube root of 16.

3) Multiply the cube root of y to both the numerator and denominator.

4) Combine.

Step 8: Simplify 2∜(162x¹⁰y⁷z⁴)

1) Factor ∜x¹⁰

2) Factor ∜y⁷

3) Factor ∜z⁴