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Sofia and Victor are simplifying the radical (2 sqrt{56}). Victor believes the answer is (4 sqrt{14}). Sofia disagrees and says the answer is (16 sqrt{14}). Who is correct? What mistake was made by the student that is not correct?

A. Victor is correct; Sofia made an error in simplification.
B. Sofia is correct; Victor made an error in simplification.
C. Both are incorrect; there is a mistake in the initial simplification.
D. Both are correct; there is no mistake in the simplification process.

User Tomzie
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Final Answer:

Sofia and Victor are simplifying the radical (2 √{56}). Victor believes the answer is (4 √{14}). Sofia disagrees and says the answer is (16 √{14}). After checking their answers, we found that Sofia is correct, and Victor made an error in simplification. Thus, the correct answer is B. Sofia is correct; Victor made an error in simplification.

Step-by-step explanation:

Let's see how Sofia and Victor arrived at their answers and where they went wrong.

Victor's answer: (4 √{14})

Victor simplified the expression by taking out the common factor 2 from the radical sign and then simplifying the inner radical (√{56}) by finding its square root, which is 8 times the square root of 14. This gives us the final answer of (4 √{14}).

Sofia's answer: (16 √{14})

Sofia also simplified the expression by taking out the common factor 2 from the radical sign. However, instead of simplifying the inner radical, she left it as it is. This gives us the final answer of (16 √{14}).

Now let's see where Victor went wrong. When we simplify the inner radical (√{56}), we need to find its square root, which is 8 times the square root of 14. However, Victor made a mistake by taking out a common factor of 8 from both the inner and outer radical signs, which is not correct. The correct way to simplify this expression would be to take out a common factor of 2 from both the inner and outer radical signs and then find the square root of 56, which is 8 times the square root of 14. This gives us Sofia's answer of (16 √{14}).

In summary, Sofia's answer is correct because she correctly simplified the expression by taking out a common factor of 2 from both the inner and outer radical signs and leaving the inner radical as it is. Victor's answer is incorrect because he took out a common factor of 8 from both the inner and outer radical signs, which is not correct when simplifying this type of expression.

Thus, the correct answer is B. Sofia is correct; Victor made an error in simplification.

User Lynn
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