If 49 is subtracted from the square of a number, then the result obtained is 576. What is the number ?

Options

A. 24
B. 25
C. 23
D. 27

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the variable
Let the unknown number be represented by \( x \).

**Hint:** When dealing with unknowns, it's helpful to assign a variable to represent it.

### Step 2: Write the equation based on the problem statement
According to the problem, if 49 is subtracted from the square of the number, the result is 576. This can be expressed mathematically as:
\[ x^2 - 49 = 576 \]

**Hint:** Translate the words of the problem into a mathematical equation.

### Step 3: Rearrange the equation
To isolate \( x^2 \), add 49 to both sides of the equation:
\[ x^2 = 576 + 49 \]

**Hint:** To solve for a variable, you often need to rearrange the equation.

### Step 4: Perform the addition
Calculate the right side:
\[ x^2 = 625 \]

**Hint:** Make sure to perform arithmetic operations carefully.

### Step 5: Take the square root
To find \( x \), take the square root of both sides:
\[ x = \sqrt{625} \]

**Hint:** Remember that taking the square root can yield both positive and negative results.

### Step 6: Calculate the square root
The square root of 625 is:
\[ x = 25 \quad \text{or} \quad x = -25 \]

**Hint:** Check if the context of the problem allows for negative solutions.

### Step 7: Determine the appropriate solution
Since the problem does not specify that the number must be negative, we take the positive solution:
\[ x = 25 \]

**Hint:** In many real-world problems, negative solutions may not be applicable.

### Final Answer
The number is \( 25 \).

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