If `(10.15)^(2)` = 103.0225, then the value of `sqrt(1.030225) + sqrt(10302.25)` is

Options

A. 1025.15
B. 103.515
C. 102.515
D. `102.0515`

Answer

To solve the problem, we need to find the value of \( \sqrt{1.030225} + \sqrt{10302.25} \).

### Step 1: Calculate \( \sqrt{1.030225} \)

Given that \( (10.15)^2 = 103.0225 \), we can rewrite \( 1.030225 \) as follows:

\[ 1.030225 = \frac{103.0225}{100} \]

Now, we can find the square root:

\[ \sqrt{1.030225} = \sqrt{\frac{103.0225}{100}} = \frac{\sqrt{103.0225}}{\sqrt{100}} = \frac{10.15}{10} = 1.015 \]

### Step 2: Calculate \( \sqrt{10302.25} \)

Next, we can express \( 10302.25 \) in a similar way:

\[ 10302.25 = 103.0225 \times 100 \]

Now, we find the square root:

\[ \sqrt{10302.25} = \sqrt{103.0225 \times 100} = \sqrt{103.0225} \times \sqrt{100} = 10.15 \times 10 = 101.5 \]

### Step 3: Add the two square roots

Now we can add the results from Step 1 and Step 2:

\[ \sqrt{1.030225} + \sqrt{10302.25} = 1.015 + 101.5 = 102.515 \]

### Final Answer

Thus, the value of \( \sqrt{1.030225} + \sqrt{10302.25} \) is:

\[ \boxed{102.515} \]