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

Simplify the following expression. (sqrt(11) * sqrt(50)) / sqrt(2) = Enter your answer
Transcript text: Simplify the following expression. $\frac{\sqrt{11} \cdot \sqrt{50}}{\sqrt{2}}=$ Enter your answer
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Solution

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Solution Steps

To simplify the given expression 11502\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.

Step 1: Combine the Radicals in the Numerator

We start by combining the radicals in the numerator: 1150=1150=550 \sqrt{11} \cdot \sqrt{50} = \sqrt{11 \cdot 50} = \sqrt{550}

Step 2: Simplify the Expression

Next, we simplify the given expression: 5502=5502=275 \frac{\sqrt{550}}{\sqrt{2}} = \sqrt{\frac{550}{2}} = \sqrt{275}

Step 3: Rationalize the Denominator

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

Step 4: Calculate the Numerical Value

We calculate the numerical value of 275\sqrt{275}: 27516.5831 \sqrt{275} \approx 16.5831

Final Answer

16.5831 \boxed{16.5831}

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