Let x be the greater real root of x^2 − 365 = 364 and y satisfy y − √324 = √81. Compare x and y.

Introduction / Context: We compare exact numerical values derived from simple square roots. The equations are arranged to yield integers after evaluation, simplifying the comparison.

Given Data / Assumptions:

• x^2 − 365 = 364 ⇒ x^2 = 729 ⇒ roots ±27; greater x = 27.
• y − √324 = √81 ⇒ y − 18 = 9 ⇒ y = 27.

Concept / Approach: Evaluate each side carefully. √324 = 18 and √81 = 9. Then solve the simple linear relation for y and compare with x.

Step-by-Step Solution:

Verification / Alternative check: Substitutions confirm both equations are satisfied by 27.

Why Other Options Are Wrong: Strict inequalities do not hold since equality is exact.

Common Pitfalls: Misreading the radicals or arithmetic around subtracting and adding 18 and 9.

Final Answer: If x ≥ y