Questions: Simplify. √(42 s) · √(7 s) =

Solution Steps

Multiply the two square roots together: \[ \sqrt{42s} \cdot \sqrt{7s} = \sqrt{(42s)(7s)}. \]

Multiply the numbers and the variables separately: \[ (42s)(7s) = 42 \cdot 7 \cdot s \cdot s = 294s^2. \] So, the expression becomes: \[ \sqrt{294s^2}. \]

Factor \(294\) and \(s^2\) to simplify: \[ 294 = 49 \cdot 6 = 7^2 \cdot 6, \] and \[ s^2 = s^2. \] Thus, the expression becomes: \[ \sqrt{7^2 \cdot 6 \cdot s^2} = \sqrt{7^2} \cdot \sqrt{6} \cdot \sqrt{s^2}. \]

Evaluate the square roots: \[ \sqrt{7^2} = 7, \quad \sqrt{s^2} = s, \quad \text{and} \quad \sqrt{6} = \sqrt{6}. \] Combine these results: \[ 7 \cdot \sqrt{6} \cdot s = 7s\sqrt{6}. \]

Final Answer