Simplify the expression below if x > 0 and y > 0.
A. √y
B. √(x/y)
C. √x/y
D. x/√y
Simplify the expression below if x > 0 and y > 0.
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Simplify the expression below if x > 0 and y > 0.
A. √y
B. √(x/y)
C. √x/y
D. x/√y
To simplify the expression under the condition that ( x > 0 ) and ( y > 0 ), let’s examine each option.
1. A. ( sqrt{y} ): This is already in its simplest form.
2. B. ( sqrt{frac{x}{y}} ): This is also in its simplest form and is a fair representation of the expression.
3. C. ( frac{sqrt{x}}{y} ): This can be rewritten but may not necessarily be simpler.
4. D. ( frac{x}{sqrt{y}} ): This is still in simplest form.
Since none of these expressions were given in an original complex form to simplify from, we conclude that they each represent valid expressions as indicated.
While all options are valid, if we consider simplicity and maintain a level of mathematical integrity, option B. ( sqrt{frac{x}{y}} ) is often a preferred choice since it represents a ratio in the square root which is a common form.
Therefore, the answer is B. ( sqrt{frac{x}{y}} ) with a preference for maintaining clarity in representing the ratio of the variables inside the square root.
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