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

Introduction / Context:
This question involves a simple quadratic equation arising from a sentence about squares and subtraction. You are told that when 49 is subtracted from the square of a number, the result is 576. From this, you must determine the original number. The problem tests basic algebra skills and understanding of square roots.

Given Data / Assumptions:

- Let the unknown number be n. - The expression n^2 - 49 represents the square of the number minus 49. - We are told that n^2 - 49 = 576. - We are looking for a positive integer solution as suggested by the options.

Concept / Approach:
The key idea is to convert the verbal description into an algebraic equation and then isolate n. After adding 49 to both sides, we obtain n^2 on one side equal to a known value. Taking the positive square root of that value (because the context suggests a positive number) gives the answer. Recognizing perfect squares and their roots is very helpful here.

Step-by-Step Solution:
Step 1: Introduce a variable n for the number. The condition becomes n^2 - 49 = 576. Step 2: Add 49 to both sides of the equation to isolate the square term: n^2 = 576 + 49. Step 3: Compute 576 + 49 = 625. Step 4: Now we have n^2 = 625. Step 5: Take square roots of both sides: n = ±√625. Step 6: Compute √625. Since 25 * 25 = 625, √625 = 25. Step 7: Thus n = 25 or n = -25 formally, but the options list only positive numbers and the usual interpretation of such questions is the positive value. Step 8: Therefore the required number is 25.

Verification / Alternative check:
Verify by substituting n = 25 into the original statement. Compute the square: 25^2 = 625. Subtract 49: 625 - 49 = 576, which matches the given result. For completeness, note that n = -25 also satisfies the equation algebraically, since (-25)^2 is also 625, but this value is not among the listed options and problems of this type usually intend the positive root.

Why Other Options Are Wrong:
If n = 24, then n^2 - 49 = 576 - 49 = 527, not 576. If n = 23, n^2 is 529, and 529 - 49 = 480. If n = 27, n^2 is 729, and 729 - 49 = 680. None of these match the required result of 576. Only n = 25 produces the correct value.

Common Pitfalls:
Some learners mistakenly subtract 49 from 576 instead of adding it back to get n^2. Others may forget that squaring a negative number also produces a positive result, although in this context the positive root is the relevant one. Carefully translating the sentence into n^2 - 49 = 576 and then solving step by step avoids such mistakes.

Final Answer:
The number whose square minus 49 equals 576 is 25, which corresponds to option B.