Question

radical 50v^5 times radical 7

Answer 1

To simplify the expression \(\sqrt{50v^5} \times \sqrt{7}\), you can combine the radicals:

\[
\sqrt{50v^5} \times \sqrt{7} = \sqrt{50v^5 \times 7}
\]

Now calculate \(50 \times 7\):

\[
50 \times 7 = 350
\]

So the expression becomes:

\[
\sqrt{350v^5}
\]

Next, we can break down \(350v^5\) into its prime factors and perfect squares:

\[
350 = 25 \times 14 = 25 \times 2 \times 7
\]
\[
v^5 = v^4 \times v = (v^2)^2 \times v
\]

Now substituting back, we have:

\[
\sqrt{350v^5} = \sqrt{25 \times 14 \times v^4 \times v}
\]

Using the property of square roots, we can separate the perfect square:

\[
\sqrt{350v^5} = \sqrt{25} \times \sqrt{14} \times \sqrt{v^4} \times \sqrt{v}
\]

Calculating the square roots:

\[
\sqrt{25} = 5, \quad \sqrt{v^4} = v^2
\]

Now we can combine these results:

\[
\sqrt{350v^5} = 5v^2 \sqrt{14v}
\]

Thus, the final simplified form of the expression is:

\[
5v^2 \sqrt{14v}
\]