Questions: (a) ∛(-64)= □ (b) ∜(-625)=

Solution Steps

The cube root of \(-64\) can be expressed as: \[ \sqrt[3]{-64} = -4 \] This is a real number since cube roots of negative numbers yield real results.

The fourth root of \(-625\) is not a real number. In the complex number system, it can be expressed as: \[ \sqrt[4]{-625} = \sqrt[4]{625} \cdot \sqrt[4]{-1} = 5 \cdot \left( \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}j \right) = 3.5355 + 3.5355j \] However, since we are only interested in real numbers, we conclude that this expression does not yield a real result.

Final Answer