Simplify the radical expression: √289 − √625 ÷ √25, using standard order of operations (division before subtraction). Provide the exact integer result.

Introduction / Context:This test checks the correct application of order of operations to square roots and division. Remember that division is performed before subtraction unless parentheses indicate otherwise.

Given Data / Assumptions:

• Expression: √289 − √625 ÷ √25.
• Standard order: evaluate square roots, perform division, then subtract.
• All roots are principal (non-negative) square roots.

Concept / Approach:First compute each square root exactly. Then divide the results as indicated. Finally, finish with the subtraction. Avoid prematurely subtracting before handling the division to the right.

Step-by-Step Solution:

Verification / Alternative check:Rewriting: 17 − (25/5) = 17 − 5 = 12. No other operations apply, confirming the result.

Why Other Options Are Wrong:17 corresponds to ignoring the division term. 15 and 10 arise from mixing addition or miscomputing 25/5. −8/5 comes from an incorrect ordering or sign error.

Common Pitfalls:Subtracting 25 first or treating √625 ÷ √25 as √(625/25) only after subtraction; although √625 ÷ √25 equals √(625/25) numerically, the subtraction must wait until the division is completed.

Final Answer:12