Rationalize the Denominator and Simplify $\sqrt { \frac { 75 x ^ { 3 } } { y 5 } }$

question 166

Multiple Choice

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
- $\sqrt { \frac { 75 x ^ { 3 } } { y 5 } }$

• A) \(\frac { x \sqrt { 75 x y } } { y 3 }\)
• B) \(\frac { 5 x ^ { 3 } \sqrt { 3 } } { y 5 }\)
• C) \(\frac { 5 x } { y 2 } \sqrt { \frac { 3 x } { y } }\)
• D) \(\frac { 5 x \sqrt { 3 x y } } { y 3 }\)

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Definitions:

Probability

A measure of the likelihood that an event will occur, ranging from 0 (impossibility) to 1 (certainty).

Expected Utility Function

A concept in economics that represents an individual's preference for certain outcomes over others, calculated as a weighted average of the utility of all possible outcomes, based on their probabilities.

Utility Function

In economics, a mathematical representation that ranks individuals' preferences over sets of goods and services, indicating the level of satisfaction or utility they obtain.

Risk Neutral

A risk neutral person or entity is indifferent between choices with different levels of risk, focusing solely on the expected outcome without concern for the variability of returns.