The number, whose square is equal to the difference between the squares of 975 and 585, is :

Options

A. 780
B. 390
C. 1560
D. 130

Answer

To solve the problem step by step, we need to find the number whose square is equal to the difference between the squares of 975 and 585.

### Step 1: Understand the problem
We need to find a number \( A \) such that:
\[ A^2 = 975^2 - 585^2 \]

### Step 2: Use the difference of squares formula
We can use the difference of squares formula, which states:
\[ a^2 - b^2 = (a + b)(a - b) \]
In our case, \( a = 975 \) and \( b = 585 \). Therefore:
\[ 975^2 - 585^2 = (975 + 585)(975 - 585) \]

### Step 3: Calculate \( 975 + 585 \) and \( 975 - 585 \)
Now, we calculate:
\[ 975 + 585 = 1560 \]
\[ 975 - 585 = 390 \]

### Step 4: Substitute back into the formula
Now we substitute these values back into the difference of squares formula:
\[ A^2 = (975^2 - 585^2) = 1560 \times 390 \]

### Step 5: Calculate \( 1560 \times 390 \)
Next, we calculate the product:
\[ A^2 = 1560 \times 390 \]

### Step 6: Simplify the multiplication
We can break down the multiplication:
\[ 1560 \times 390 = 1560 \times (300 + 90) = 1560 \times 300 + 1560 \times 90 \]
Calculating each part:
\[ 1560 \times 300 = 468000 \]
\[ 1560 \times 90 = 140400 \]
Adding these together:
\[ A^2 = 468000 + 140400 = 608400 \]

### Step 7: Find \( A \)
Now we need to find \( A \):
\[ A = \sqrt{608400} \]
Calculating the square root:
\[ A = 780 \]

### Final Answer
The number whose square is equal to the difference between the squares of 975 and 585 is:
\[ \boxed{780} \]