Determine which two values the following expression is between.

Question

2√5

A.
4.44 and 4.45
B.
4.47 and 4.48
C.
4.45 and 4.46
D.
4.46 and 4.47

Answer 1

To determine the range of the expression \( 2\sqrt{5} \), we first need to calculate the value of \( \sqrt{5} \).

The approximate value of \( \sqrt{5} \) is about 2.236.

Now we can calculate \( 2\sqrt{5} \):

\[ 2\sqrt{5} \approx 2 \times 2.236 = 4.472 \]

Now we will compare this value with the options given:

• Option A: 4.44 and 4.45 (4.44 < 4.472 < 4.45) - Not true
• Option B: 4.47 and 4.48 (4.47 < 4.472 < 4.48) - True
• Option C: 4.45 and 4.46 (4.45 < 4.472 < 4.46) - Not true
• Option D: 4.46 and 4.47 (4.46 < 4.472 < 4.47) - Not true

The correct option is B: 4.47 and 4.48.