Question

Express in simplest radical form

(Sqrt)5(sqrt)30

Answer 1

To simplify \(\sqrt{5} \cdot \sqrt{30}\), we can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\).

So, we have:

\[
\sqrt{5} \cdot \sqrt{30} = \sqrt{5 \cdot 30}
\]

Now, calculate \(5 \cdot 30\):

\[
5 \cdot 30 = 150
\]

Therefore:

\[
\sqrt{5} \cdot \sqrt{30} = \sqrt{150}
\]

Next, we can simplify \(\sqrt{150}\). We can factor \(150\) as follows:

\[
150 = 25 \cdot 6 = 5^2 \cdot 6
\]

Now, we can simplify \(\sqrt{150}\):

\[
\sqrt{150} = \sqrt{25 \cdot 6} = \sqrt{25} \cdot \sqrt{6} = 5\sqrt{6}
\]

Thus, the expression \(\sqrt{5} \cdot \sqrt{30}\) in simplest radical form is:

\[
\boxed{5\sqrt{6}}
\]