2024 AMC 10B Problems/Problem 13

Problem

Positive integers $x$ and $y$ satisfy the equation $\sqrt{x} + \sqrt{y} = \sqrt{1183}$ . What is the minimum possible value of $x+y$ .

$\textbf{(A) } 585 \qquad\textbf{(B) } 595 \qquad\textbf{(C) } 623 \qquad\textbf{(D) } 700 \qquad\textbf{(E) } 791$

Solution 1

(Not yet conclusive plz add more stuff) $\sqrt{1183} = 13 \sqrt7 = 6\sqrt7 + 7\sqrt7 = \sqrt{252} + \sqrt{343}$ . $252 + 343 = \boxed{\textbf{(B) }595}$

2024 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
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2024 AMC 10B Problems/Problem 13

Problem

Solution 1

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