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

Simplify.
√(42 s) · √(7 s) =
Transcript text: Simplify. \[ \sqrt{42 s} \cdot \sqrt{7 s}= \]
failed

Solution

failed
failed

Solution Steps

Step 1: Combine the square roots

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: \[ \sqrt{7^2 \cdot 6 \cdot s^2} = \sqrt{7^2} \cdot \sqrt{6} \cdot \sqrt{s^2}. \]

Step 4: Simplify the square roots

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

\(\boxed{7s\sqrt{6}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful