Question
The value of √12 is in between which two integers?
3 and 4
11 and 13
6 and 7
25 and 36
3 and 4
11 and 13
6 and 7
25 and 36
Answers
GPT-4o mini
To find the value of \( \sqrt{12} \) and determine between which two integers it lies, we can first calculate it.
1. We know that:
\[
3^2 = 9
\]
\[
4^2 = 16
\]
Since \( 9 < 12 < 16 \), it follows that:
\[
3 < \sqrt{12} < 4
\]
Next, we can confirm this by approximating \( \sqrt{12} \).
2. We can express \( \sqrt{12} \) as:
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
\]
3. Approximate \( \sqrt{3} \) (which is approximately \( 1.732 \)):
\[
2\sqrt{3} \approx 2 \times 1.732 \approx 3.464
\]
This confirms that:
\[
3 < \sqrt{12} < 4
\]
Thus, the value of \( \sqrt{12} \) is between the integers 3 and 4.
Therefore, the answer is **3 and 4**.
1. We know that:
\[
3^2 = 9
\]
\[
4^2 = 16
\]
Since \( 9 < 12 < 16 \), it follows that:
\[
3 < \sqrt{12} < 4
\]
Next, we can confirm this by approximating \( \sqrt{12} \).
2. We can express \( \sqrt{12} \) as:
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
\]
3. Approximate \( \sqrt{3} \) (which is approximately \( 1.732 \)):
\[
2\sqrt{3} \approx 2 \times 1.732 \approx 3.464
\]
This confirms that:
\[
3 < \sqrt{12} < 4
\]
Thus, the value of \( \sqrt{12} \) is between the integers 3 and 4.
Therefore, the answer is **3 and 4**.