Donna and Donald are plotting 7−28−−√

on a number line. Their responses are below.

Which student is correct?

Responses

Donna
Donna

Donald
Donald
Question 2
Identify the correct reasoning behind the correct location.
Responses

Donald is correct because he determined 28−−√
falls between the values of 5 and 6.
Donald is correct because he determined square root of 28 falls between the values of 5 and 6.

Donna is correct because she determined 28−−√
falls between the values of 5 and 6. Since 7-5 = 2 and 7-6 =1, the correct location is between 1 and 2.
Donna is correct because she determined square root of 28 falls between the values of 5 and 6. Since 7-5 = 2 and 7-6 =1, the correct location is between 1 and 2.

Donna is correct because she determined 28−−√
falls between the values of 5 and 6.
Donna is correct because she determined square root of 28 falls between the values of 5 and 6.

Donald is correct because he determined 28−−√
falls between the values 5 and 6. Since 7-5 = 2 and 7-6 = 1 the correct location is between 1 and 2.

1 answer

To determine who is correct, let's first calculate the square root of 28 and then evaluate \( 7 - \sqrt{28} \).

  1. Calculating \( \sqrt{28} \):

    • We know \( \sqrt{25} = 5 \) and \( \sqrt{36} = 6 \), so \( \sqrt{28} \) is between 5 and 6.
    • A better approximation of \( \sqrt{28} \) can be found: \[ \sqrt{28} \approx 5.29 \]
  2. Calculating \( 7 - \sqrt{28} \): \[ 7 - \sqrt{28} \approx 7 - 5.29 = 1.71 \]

Thus, \( 7 - \sqrt{28} \) is approximately 1.71, which fits between 1 and 2 on a number line.

Now, let's evaluate the students' responses:

  • Donald states that \( \sqrt{28} \) falls between 5 and 6. This is correct.
  • Donna correctly states that \( \sqrt{28} \) falls between 5 and 6, but she misinterprets the result to say \( 7 - \sqrt{28} \) is between 1 and 2, which is correct, but her reasoning regarding \( 7 - 5 \) and \( 7 - 6 \) is misleading.

Conclusion:

Both students are correct in identifying that \( \sqrt{28} \) is between 5 and 6. The correct interpretation of the location of \( 7 - \sqrt{28} \) is consistent with both students, but given that both misplace the final interpretation based on their individual reasoning, it's important to note that Donald gives clearer reasoning in determining that \( \sqrt{28} \) lies between 5 and 6 without confusion.

Thus, Donald is correct, and the best response is: "Donald is correct because he determined the square root of 28 falls between the values of 5 and 6."