If `(99)^2` is added to the square of a number, the answer so obtained is 20002. What is the number?

Options

A. 100
B. 104
C. 102
D. 101

Answer

To solve the problem, we need to find the number \( x \) such that:

\[ (99)^2 + x^2 = 20002 \]

### Step 1: Calculate \( (99)^2 \)

First, we calculate the square of 99:

\[ (99)^2 = 9801 \]

### Step 2: Set up the equation

Now, we substitute \( (99)^2 \) into the equation:

\[ 9801 + x^2 = 20002 \]

### Step 3: Isolate \( x^2 \)

Next, we need to isolate \( x^2 \) by subtracting 9801 from both sides:

\[ x^2 = 20002 - 9801 \]

### Step 4: Perform the subtraction

Now we perform the subtraction:

\[ x^2 = 20002 - 9801 = 10201 \]

### Step 5: Take the square root

To find \( x \), we take the square root of both sides:

\[ x = \sqrt{10201} \]

### Step 6: Calculate \( \sqrt{10201} \)

Calculating the square root gives us:

\[ x = 101 \]

### Final Answer

The number is:

\[ \boxed{101} \]

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