Answer:
6² = 36 and 12² = 144
Explanation:
You want two square numbers whose sum is 180.
Square numbers
Square numbers less than 180 are ...
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169
We can see that 36+144 = 180
The two square numbers are 36 and 144. They are, respectively, the squares of 6 and 12.
Alternate look
The factorization of 180 is ...
180 = 2² · 3² · 5
We note that 5 = 1+4, the sum of two squares, so the squares of interest are (2·3·1)² and (2·3·2)² = 36 and 144.
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Additional comment
Essentially, we have worked the problem here by "trial and error."
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