What is the result of (625 − 1/2 − 1/4)²?

• A. 4
• B. 5
• C. 2
• D. 3

To solve the expression (625 − 1/2 − 1/4)², we first need to simplify the part inside the parentheses.

Step 1: Simplifying Inside the Parentheses

Start with the subtraction:

• First, convert 1/2 and 1/4 to a common denominator. The common denominator for 2 and 4 is 4.
• 1/2 is equivalent to 2/4.
• Now, subtract: 625 - 2/4 - 1/4 = 625 - 3/4.

Calculating 625 - 3/4

To perform this subtraction, convert 625 into a fraction:

• 625 can be written as 625/1.
• Now, convert it to have a denominator of 4: 625/1 = 2500/4.
• Now, subtract: 2500/4 - 3/4 = (2500 - 3)/4 = 2497/4.

Step 2: Squaring the Result

Now we need to square the result:

• (2497/4)² = 2497² / 4² = 6245009 / 16.

Final Calculation

Now, we can evaluate the options given:

• A. 4
• B. 5
• C. 2
• D. 3

The value of 6245009 / 16 is much larger than any of the options provided. Therefore, none of the options A, B, C, or D are correct.