The value of `(17.5)^2` is

Options

A. `306 `
B. `306.25`
C. `306.2`
D. `306.3`

Answer

To find the value of \( (17.5)^2 \), we can follow these steps:

### Step 1: Calculate \( 17.5 \times 17.5 \)

First, we multiply \( 17.5 \) by itself:

\[ 17.5 \times 17.5 \]

### Step 2: Use the formula for squaring a binomial

We can use the formula \( (a + b)^2 = a^2 + 2ab + b^2 \). Here, we can express \( 17.5 \) as \( 17 + 0.5 \):

\[ (17 + 0.5)^2 = 17^2 + 2 \times 17 \times 0.5 + 0.5^2 \]

### Step 3: Calculate each term

1. Calculate \( 17^2 \):
\[ 17^2 = 289 \]

2. Calculate \( 2 \times 17 \times 0.5 \):
\[ 2 \times 17 \times 0.5 = 17 \]

3. Calculate \( 0.5^2 \):
\[ 0.5^2 = 0.25 \]

### Step 4: Add the results together

Now, we add all the results together:

\[ 289 + 17 + 0.25 = 306.25 \]

### Step 5: Round to three significant figures

Since we need the answer to three significant figures, we look at \( 306.25 \). The third significant figure is 6, and the next digit (5) indicates that we round up:

\[ 306.25 \rightarrow 306.3 \text{ (to three significant figures)} \]

### Step 6: Final answer

Thus, the value of \( (17.5)^2 \) rounded to three significant figures is:

\[ \boxed{306} \]

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