To simplify \(\sqrt{98s^4}\), we can break it down into two parts: the numerical part (98) and the variable part (\(s^4\)).
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Simplify the numerical part: \[ 98 = 49 \times 2 = 7^2 \times 2 \]
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Simplify the variable part: \[ s^4 = (s^2)^2 \]
Now we can combine these results under the square root: \[ \sqrt{98s^4} = \sqrt{49 \times 2 \times s^4} = \sqrt{49} \times \sqrt{2} \times \sqrt{s^4} \]
Calculating each square root: \[ \sqrt{49} = 7, \quad \sqrt{2} = \sqrt{2}, \quad \text{and } \sqrt{s^4} = s^2 \]
Therefore, we can now put it all together: \[ \sqrt{98s^4} = 7s^2\sqrt{2} \]
So, the simplified form of \(\sqrt{98s^4}\) is: \[ \boxed{7s^2\sqrt{2}} \]