`664sqrt(15)+75.086`

Options

A. 2900
B. 3500
C. 4000
D. 2700

Answer

To solve the expression \( 664\sqrt{15} + 75.086 \), we will follow these steps:

### Step 1: Estimate the value of \( \sqrt{15} \)
We know that \( \sqrt{15} \) is between \( \sqrt{9} = 3 \) and \( \sqrt{16} = 4 \). A more precise approximation can be calculated:
\[ \sqrt{15} \approx 3.87 \]

### Step 2: Multiply \( 664 \) by \( \sqrt{15} \)
Now we will calculate \( 664 \times \sqrt{15} \):
\[ 664 \times 3.87 \approx 2575.68 \]

### Step 3: Add \( 75.086 \) to the result from Step 2
Now we add \( 75.086 \) to the result from the previous step:
\[ 2575.68 + 75.086 \approx 2650.766 \]

### Step 4: Round the result to the nearest whole number
Rounding \( 2650.766 \) gives us approximately \( 2651 \).

### Step 5: Compare with the options provided
The options given are 2900, 3500, 4000, and 2700. The closest option to our calculated value of \( 2651 \) is \( 2700 \).

### Final Answer
Thus, the approximate value of \( 664\sqrt{15} + 75.086 \) is \( 2700 \).

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