If `(19)^2` is added to a number the value so obtained is `(23)^2`. What is the number ?

Options

A. 165
B. 166
C. 178
D. None of these

Answer

To solve the problem step by step, we need to find the number \( x \) such that when \( 19^2 \) is added to it, the result is \( 23^2 \).

### Step 1: Write the equation based on the problem statement.
We know from the problem that:
\[ x + 19^2 = 23^2 \]

### Step 2: Calculate \( 19^2 \) and \( 23^2 \).
First, we calculate \( 19^2 \):
\[ 19^2 = 361 \]
Next, we calculate \( 23^2 \):
\[ 23^2 = 529 \]

### Step 3: Substitute the values into the equation.
Now we substitute these values back into the equation:
\[ x + 361 = 529 \]

### Step 4: Solve for \( x \).
To find \( x \), we need to isolate it on one side of the equation. We do this by subtracting \( 361 \) from both sides:
\[ x = 529 - 361 \]

### Step 5: Perform the subtraction.
Now we perform the subtraction:
\[ 529 - 361 = 168 \]

### Conclusion: The value of the number \( x \).
Thus, the number is:
\[ \boxed{168} \]

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