QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
# What happens when you square a cubed root or cube a square root? Provide examples and show your work.
Example 1: Squaring a cubed root
(\sqrt[3]{x})^{2}
Example 2: Cubing a square root
(\sqrt{x})^{3}
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Step 1I'll solve this problem step by step, demonstrating how to manipulate these nested radical expressions.
Example 1: Squaring a Cubed Root $$(\sqrt[3]{x})^{2}
Step 2: Understand the expression
- We have a cubed root of x, which is then squared - This means we're taking the cube root of x and then squaring the result
Final Answer
1. (\sqrt[3]{x})^{2} = x^{\frac{2}{3}} 2. (\sqrt{x})^{3} = x^{\frac{3}{2}} Key Insights: - When squaring a cubed root, the exponent becomes \frac{2}{3} - When cubing a square root, the exponent becomes \frac{3}{2} - The general rule is to multiply the original fractional exponent by the new power
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