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Finding Square Root through Prime Factorisation

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Question

(Exploration) Find all perfect squares from 1 to 500, each of which is a sum of two perfect squares.

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Solution

It can be observed that:

5² = 3² + 4² [25 = 9 + 16]

10² = 6² + 8² [100 = 36 + 64]

13² = 5² + 12² [169 = 25 + 144]

17² = 8² + 15² [289 = 64 + 225]

Thus, the required perfect squares are 25, 100, 169 and 289.

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