Multiply the two square roots together:
\[
\sqrt{42s} \cdot \sqrt{7s} = \sqrt{(42s)(7s)}.
\]
Step 2: Simplify the expression inside the square root
Multiply the numbers and the variables separately:
\[
(42s)(7s) = 42 \cdot 7 \cdot s \cdot s = 294s^2.
\]
So, the expression becomes:
\[
\sqrt{294s^2}.
\]
Step 3: Break down the square root
Factor \(294\) and \(s^2\) to simplify:
\[
294 = 49 \cdot 6 = 7^2 \cdot 6,
\]
and
\[
s^2 = s^2.
\]
Thus, the expression becomes:
\[
\sqrt{7^2 \cdot 6 \cdot s^2} = \sqrt{7^2} \cdot \sqrt{6} \cdot \sqrt{s^2}.
\]