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Home » Thus, the area of the square is \(\boxed50\). - Crosslake

Thus, the area of the square is \(\boxed50\). - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: What is the sum of all positive divisors of \( 360 \) that are perfect squares?

📌 First, factor \( 360 \):

📌 = 36 \times 10 = (2^2 \cdot 3^2) \cdot (2 \cdot 5) = 2^3 \cdot 3^2 \cdot 5^1

📌 We seek divisors of \( 360 \) that are perfect squares. A divisor is a perfect square if all exponents in its prime factorization are even.

📌 Let a divisor \( d = 2^a \cdot 3^b \cdot 5^c \) be a perfect square, with:

📌 \( a \in \{0, 2\} \) (since \( a \leq 3 \), and even)

📌 \( b \in \{0, 2\} \) (since \( b \leq 2 \), even)

📌 \( c \in \{0\} \) (since \( c \leq 1 \), and only even choice is 0)

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