Question

Multiply. Assume s is greater than or equal to zero, and write your answer in simplest form.
√21s x √21

Answer 1

To multiply the expressions \( \sqrt{21s} \) and \( \sqrt{21} \), you use the property of square roots that states:

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

Applying this property, we can rewrite the multiplication as follows:

\[
\sqrt{21s} \times \sqrt{21} = \sqrt{(21s) \times 21}
\]

Now, multiply the quantities inside the square root:

\[
21s \times 21 = 441s
\]

Thus, we have:

\[
\sqrt{21s} \times \sqrt{21} = \sqrt{441s}
\]

Next, we can simplify \( \sqrt{441} \). Since \( 441 = 21^2 \), we have:

\[
\sqrt{441} = 21
\]

Putting it together, we find:

\[
\sqrt{441s} = \sqrt{441} \times \sqrt{s} = 21\sqrt{s}
\]

Therefore, the final simplified result is:

\[
\boxed{21\sqrt{s}}
\]