Simplify. Assume s is greater than or equal to zero.

square root 98s4

1 answer

To simplify \(\sqrt{98s^4}\), we can break it down into two parts: the numerical part (98) and the variable part (\(s^4\)).

  1. Simplify the numerical part: \[ 98 = 49 \times 2 = 7^2 \times 2 \]

  2. 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: \[ \boxed{7s^2\sqrt{2}} \]