Question
Determine which two values the following irrational number is between.
√23
A.
is between 6.3 and 7.3
B.
is between 4.3 and 5.3
C.
is between 5.3 and 6.3
D.
is between 3.3 and 4.3
√23
A.
is between 6.3 and 7.3
B.
is between 4.3 and 5.3
C.
is between 5.3 and 6.3
D.
is between 3.3 and 4.3
Answers
GPT-4o mini
To determine the value of \( \sqrt{23} \) and find the correct range from the options provided, we can start by estimating the square root.
We know that:
- \( 4^2 = 16 \)
- \( 5^2 = 25 \)
Since \( 16 < 23 < 25 \), it follows that \( 4 < \sqrt{23} < 5 \).
Next, we can narrow it down further. Now we can check the squares of numbers between 4 and 5 to get a more precise estimate:
- \( 4.5^2 = 20.25 \) (which is less than 23)
- \( 4.6^2 = 21.16 \) (which is still less than 23)
- \( 4.7^2 = 22.09 \) (which is still less than 23)
- \( 4.8^2 = 23.04 \) (which is more than 23)
Thus, we now know \( 4.7 < \sqrt{23} < 4.8 \).
Therefore, the correct answer to the question is that \( \sqrt{23} \) is between:
**D. is between 4.3 and 5.3**.
We know that:
- \( 4^2 = 16 \)
- \( 5^2 = 25 \)
Since \( 16 < 23 < 25 \), it follows that \( 4 < \sqrt{23} < 5 \).
Next, we can narrow it down further. Now we can check the squares of numbers between 4 and 5 to get a more precise estimate:
- \( 4.5^2 = 20.25 \) (which is less than 23)
- \( 4.6^2 = 21.16 \) (which is still less than 23)
- \( 4.7^2 = 22.09 \) (which is still less than 23)
- \( 4.8^2 = 23.04 \) (which is more than 23)
Thus, we now know \( 4.7 < \sqrt{23} < 4.8 \).
Therefore, the correct answer to the question is that \( \sqrt{23} \) is between:
**D. is between 4.3 and 5.3**.