Use the quotient rule to simplify. Assume that all variables represent positive real numbers.

(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals
as needed.)

Ask by Murray Reid. in the United States

Mar 13,2025

Question

Use the quotient rule to simplify. Assume that all variables represent positive real numbers.

(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals
as needed.)

Ask by Murray Reid. in the United States

Mar 13,2025

UpStudy AI · Accepted Answer

We start with the expression  
$$
\sqrt{\frac{x^2 y}{225}}
$$  
and apply the quotient rule for square roots, which states that  
$$
\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}},
$$  
for $$ a, b > 0 $$. Thus, we have  
$$
\sqrt{\frac{x^2 y}{225}} = \frac{\sqrt{x^2 y}}{\sqrt{225}}.
$$

Next, compute the denominator:
$$
\sqrt{225} = 15.
$$

Now, simplify the numerator. Since $$ x $$ is positive, we know that  
$$
\sqrt{x^2} = x.
$$
Thus,
$$
\sqrt{x^2 y} = \sqrt{x^2} \sqrt{y} = x \sqrt{y}.
$$

Putting these together, our expression becomes:
$$
\frac{x \sqrt{y}}{15}.
$$

This is the simplified form of the original expression.
$$ \frac{x \sqrt{y}}{15} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers.

(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals
as needed.)

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Use the quotient rule to simplify. Assume that all variables represent positive real numbers. (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.)

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Use the quotient rule to simplify. Assume that all variables represent positive real numbers.

(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals
as needed.)