`(15.01)^(2)xxsqrt(730)=?`

Options

A. 6125
B. 6225
C. 6200
D. 6075

Explanation

To solve the expression \( (15.01)^2 \times \sqrt{730} \), we can break it down into manageable steps.

### Step 1: Calculate \( (15.01)^2 \)

First, we need to find the square of \( 15.01 \):

\[ (15.01)^2 = 15.01 \times 15.01 \]

To simplify this calculation, we can use the approximation \( 15.01 \approx 15 \):

\[ (15)^2 = 15 \times 15 = 225 \]

Since \( 15.01 \) is slightly more than \( 15 \), \( (15.01)^2 \) will be slightly more than \( 225 \). However, for our calculations, we will consider it as \( 225 \) for now.

### Step 2: Calculate \( \sqrt{730} \)

Next, we need to find the square root of \( 730 \). We can approximate this value.

The perfect squares near \( 730 \) are \( 729 \) (which is \( 27^2 \)) and \( 784 \) (which is \( 28^2 \)). Therefore, we can estimate:

\[ \sqrt{730} \approx 27 \]

### Step 3: Multiply the results

Now we will multiply the results from Step 1 and Step 2:

\[ x = (15.01)^2 \times \sqrt{730} \approx 225 \times 27 \]

Calculating \( 225 \times 27 \):

\[ 225 \times 27 = 6075 \]

### Final Answer

Thus, the value of \( (15.01)^2 \times \sqrt{730} \) is approximately:

\[ \boxed{6075} \]

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