Radicals and Absolute Values - Concept

Concept Concept (1)

Since any even-numbered root must be a positive number (otherwise it is imaginary), absolute value must be used when simplifying roots with variables, which ensures the answer is positive. When working with radical expressions this requirement does not apply to any odd root because odd roots exist for negative numbers. Additionally, absolute value is not needed if an even number of a variable come out of the root - the answer must be positive.

Sample Sample Problems (4)

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Radicals and Absolute Values - Problem 1

Simplify:

75x³y⁸z⁵
Problem 1
How to simplify a square root using absolute values.
Radicals and Absolute Values - Problem 2

Simplify:

32x⁵y¹⁰z¹⁵
Problem 2
How to simplify a fourth root using absolute values.
Radicals and Absolute Values - Problem 3

Simplify:

-64x³y⁷z⁵
Problem 3
How to simplify an odd root by not using absolute values.
Radicals and Absolute Values - Problem 4
Problem 4
When to use absolute values in simplifying radicals.