Question

Use the quotient rule to simplify the expression. Assume that x > 0.
squareroot 18x^3/squareroot 2x

squareroot 18x^3/squareroot 2x = blank

Answer 1

To simplify the expression \(\frac{\sqrt{18x^3}}{\sqrt{2x}}\), we can use the property of square roots that states \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\). Therefore, we can rewrite the expression as:

\[
\frac{\sqrt{18x^3}}{\sqrt{2x}} = \sqrt{\frac{18x^3}{2x}}
\]

Now, simplify the fraction inside the square root:

\[
\frac{18x^3}{2x} = \frac{18}{2} \cdot \frac{x^3}{x} = 9x^2
\]

So we have:

\[
\sqrt{\frac{18x^3}{2x}} = \sqrt{9x^2}
\]

Now, we can take the square root:

\[
\sqrt{9x^2} = \sqrt{9} \cdot \sqrt{x^2} = 3x
\]

Thus, the simplified expression is:

\[
\frac{\sqrt{18x^3}}{\sqrt{2x}} = 3x
\]

Therefore, the final answer is:

\[
3x
\]