Find the Domain cube root of 27y^6

Problem

√(3,27*y6)

Solution

1. Identify the type of root in the expression. The expression is a cube root, which is an odd root.

2. Determine the restriction for odd roots. Unlike square roots or other even roots, odd roots are defined for all real numbers, including negative values.

3. Analyze the radicand 27*y6 Since 27 is a constant and y6 is defined for all real values of y there are no values that make the expression undefined.

4. Conclude that the domain consists of all real numbers.

Final Answer

Domain: *(−∞,∞)

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