Question

Multiply. Assume x is greater than or equal to zero, and write your answer in simplest form.
√5x^3 * √2x^4

Answer 1

To multiply \(\sqrt{5x^3}\) and \(\sqrt{2x^4}\), you can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}\).

So we have:

\[
\sqrt{5x^3} \cdot \sqrt{2x^4} = \sqrt{(5x^3)(2x^4)}
\]

Now, multiply the terms inside the square root:

\[
(5x^3)(2x^4) = 10x^{3+4} = 10x^7
\]

Now we can simplify the square root:

\[
\sqrt{10x^7} = \sqrt{10} \cdot \sqrt{x^7}
\]

To simplify \(\sqrt{x^7}\), we can factor it as follows:

\[
x^7 = x^{6+1} = x^6 \cdot x
\]
Thus,
\[
\sqrt{x^7} = \sqrt{x^6 \cdot x} = \sqrt{x^6} \cdot \sqrt{x} = x^3\sqrt{x}
\]

Putting it all together:

\[
\sqrt{10x^7} = \sqrt{10} \cdot x^3 \cdot \sqrt{x} = x^3 \sqrt{10x}
\]

Therefore, the final answer in simplest form is:

\[
\boxed{x^3 \sqrt{10x}}
\]