To evaluate the student's work, let's go through the step-by-step simplification and combination of the given radicals [tex]\(4 \sqrt{50} - 2 \sqrt{8}\)[/tex].
### Step 1: Simplify each radical
The student correctly observes that:
[tex]\[ \sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} \][/tex]
[tex]\[ \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} \][/tex]
### Step 2: Apply the simplifications to the original expression
Now, substituting back into the original expression:
[tex]\[ 4 \sqrt{50} = 4 \times 5 \sqrt{2} = 20 \sqrt{2} \][/tex]
[tex]\[ 2 \sqrt{8} = 2 \times 2 \sqrt{2} = 4 \sqrt{2} \][/tex]
### Step 3: Combine the simplified terms
Now, the expression becomes:
[tex]\[ 20 \sqrt{2} - 4 \sqrt{2} = 16 \sqrt{2} \][/tex]
However, the student has the final answer as:
[tex]\[ 92 \sqrt{2} \][/tex]
### Check for Errors
Thus, the student's mistake lies in the combination of the terms within the expression. Clearly, somewhere in the steps, they missed the accurate simplification and arithmetic combination process.
Based on this analysis:
### Appropriate Choice
The appropriate choice is:
B. The student did not properly simplify the radicals.
