Evaluate cube root of 9

Problem

√(3,9)

Solution

1. Identify the expression as the cube root of the number 9, which can be written in radical form as √(3,9)

2. Rewrite the expression using a fractional exponent, where the index of the root becomes the denominator of the exponent.

3. Express the base 9 as a power of 3, noting that 9=3^2

4. Apply the power of a power rule, which states that (a^m)^n=a^(m⋅n) to simplify the exponent.

5. Determine the decimal approximation if a numerical value is required, noting that 9 is not a perfect cube.

Final Answer

√(3,9)=9^(1/3)≈2.08008

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