3√-3 3/8
As an AI language model, I cannot evaluate the expression 3√-3 3/8 as it is incomplete and unclear. Please provide the complete expression or clarify the question.
To simplify the expression 3√(-3 3/8), we need to simplify the inside of the cube root first.
Step 1: Convert the mixed number 3 3/8 to an improper fraction.
To convert the mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator.
3 3/8 = (3 * 8 + 3) / 8 = 27/8
Step 2: Simplify the expression inside the cube root.
3√(-3 3/8) = 3√(-27/8)
Step 3: Simplify the fraction inside the cube root.
To simplify the fraction, we will multiply both the numerator and denominator by (-1), which gives us:
3√[(-27 * -1) / (8 * -1)] = 3√(27/-8)
Step 4: Simplify the expression inside the cube root.
To simplify the expression, we can write it as a product of a whole number and a cube root.
3√(27/-8) = 3 * √(27/-8)
Step 5: Simplify the cube root.
√(27/-8) = √(27) / √(-8) = (√(9) * √(3)) / (√(4) * √(-2)) = (3 * √(3)) / (2i) = (3√3) / (2i)
Therefore, the simplified expression is (3√3) / (2i).