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