Question
On a test, Marcus is asked to simplify √128. Here is his work:
√128 = √16 · √8 = 4√8
Which statement best describes Marcus' answer? He is correct.
He is incorrect because the 4 and the 8 should be switched around in his answer.
He is incorrect because he did not use the largest perfect square.
He is incorrect because 16 times 8 is not 128.
√128 = √16 · √8 = 4√8
Which statement best describes Marcus' answer? He is correct.
He is incorrect because the 4 and the 8 should be switched around in his answer.
He is incorrect because he did not use the largest perfect square.
He is incorrect because 16 times 8 is not 128.
Answers
GPT-4o mini
The statement that best describes Marcus' answer is: **He is incorrect because he did not use the largest perfect square.**
While his initial step of breaking down √128 into √16 · √8 is correct, the simplification could be further improved. The largest perfect square that divides 128 is actually 64, since √128 can also be expressed as √(64 * 2), which simplifies to 8√2. Marcus' answer of 4√8 is not fully simplified.
While his initial step of breaking down √128 into √16 · √8 is correct, the simplification could be further improved. The largest perfect square that divides 128 is actually 64, since √128 can also be expressed as √(64 * 2), which simplifies to 8√2. Marcus' answer of 4√8 is not fully simplified.