To determine the range in which \( 2\sqrt{5} \) falls, we first need to approximate \( \sqrt{5} \).
Since \( \sqrt{4} = 2 \) and \( \sqrt{9} = 3 \), we know that \( \sqrt{5} \) must be between 2 and 3. A good approximation for \( \sqrt{5} \) is 2.236. Therefore, we can calculate \( 2\sqrt{5} \) as follows:
\[ 2\sqrt{5} \approx 2 \times 2.236 = 4.472 \]
Now, we compare this value to the given options:
- A. 4.46 and 4.47
- B. 4.45 and 4.46
- C. 4.44 and 4.45
- D. 4.47 and 4.48
The value \( 4.472 \) is indeed between \( 4.47 \) and \( 4.48 \).
Thus, the answer is D. 4.47 and 4.48.
3 answers