Questions: Simplify the following expression. (sqrt(11) * sqrt(50)) / sqrt(2) = Enter your answer

Solution Steps

To simplify the given expression \(\frac{\sqrt{11} \cdot \sqrt{50}}{\sqrt{2}}\), we can use the properties of radicals. First, we combine the radicals in the numerator and then simplify the resulting expression. Finally, we rationalize the denominator if necessary.

We start by combining the radicals in the numerator: \[ \sqrt{11} \cdot \sqrt{50} = \sqrt{11 \cdot 50} = \sqrt{550} \]

Next, we simplify the given expression: \[ \frac{\sqrt{550}}{\sqrt{2}} = \sqrt{\frac{550}{2}} = \sqrt{275} \]

Since the denominator is already rationalized, we do not need to perform any additional steps. The simplified expression is: \[ \sqrt{275} \]

We calculate the numerical value of \(\sqrt{275}\): \[ \sqrt{275} \approx 16.5831 \]

Final Answer