Question
Which statement is true about the square root of 28?(1 point) Responses It is between 5 and 6, probably closer to 6. It is between 5 and 6, probably closer to 6. It is between 6 and 7, probably closer to 6. It is between 6 and 7, probably closer to 6. It is between 4 and 5, probably closer to 5. It is between 4 and 5, probably closer to 5. It is between 5 and 6, probably closer to 5.
Answers
Answered by
GPT-4o mini
To determine the square root of 28, we can find the perfect squares around it.
- The square of 5 is \(5^2 = 25\).
- The square of 6 is \(6^2 = 36\).
Since 28 is between 25 and 36, we know that:
\[
5 < \sqrt{28} < 6
\]
Next, we can approximate \(\sqrt{28}\). Since 28 is closer to 25 than to 36, we would expect \(\sqrt{28}\) to be closer to 5 than to 6.
To calculate it more accurately, we can recognize that:
\[
\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}
\]
Approximating \(\sqrt{7}\), we know that:
- \(2.6^2 = 6.76\),
- \(2.7^2 = 7.29\).
Thus, \(2.6 < \sqrt{7} < 2.7\), which gives:
\[
5.2 < 2\sqrt{7} < 5.4.
\]
Therefore, we can conclude that \(\sqrt{28}\) is between 5 and 6, and we expect it to be closer to 5.
Thus, the correct statement is:
**"It is between 5 and 6, probably closer to 5."**
- The square of 5 is \(5^2 = 25\).
- The square of 6 is \(6^2 = 36\).
Since 28 is between 25 and 36, we know that:
\[
5 < \sqrt{28} < 6
\]
Next, we can approximate \(\sqrt{28}\). Since 28 is closer to 25 than to 36, we would expect \(\sqrt{28}\) to be closer to 5 than to 6.
To calculate it more accurately, we can recognize that:
\[
\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}
\]
Approximating \(\sqrt{7}\), we know that:
- \(2.6^2 = 6.76\),
- \(2.7^2 = 7.29\).
Thus, \(2.6 < \sqrt{7} < 2.7\), which gives:
\[
5.2 < 2\sqrt{7} < 5.4.
\]
Therefore, we can conclude that \(\sqrt{28}\) is between 5 and 6, and we expect it to be closer to 5.
Thus, the correct statement is:
**"It is between 5 and 6, probably closer to 5."**
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