Question

What is the product of the following expression in simplest radical form?

√81 ⋅ √16

Answer 1

To simplify the expression \(\sqrt{81} \cdot \sqrt{16}\), we can use the property of square roots that states:

\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}
\]

Applying this property to our expression gives:

\[
\sqrt{81} \cdot \sqrt{16} = \sqrt{81 \cdot 16}
\]

Now, we can calculate \(81 \cdot 16\):

\[
81 \cdot 16 = 1296
\]

Next, we find \(\sqrt{1296}\). We can determine this by recognizing that:

\[
1296 = 36^2
\]

Thus, we can take the square root:

\[
\sqrt{1296} = 36
\]

Therefore, we conclude:

\[
\sqrt{81} \cdot \sqrt{16} = 36
\]

In simplest radical form, the product of the expression is:

\[
\boxed{36}
\]