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# Roots

can a number 100 zeros 100 ones 100 twos is a perfect square? Prove it.

Note by Royston Dsouza
2 years, 5 months ago

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No. Hint:- Look at divisibility by 3 and 9.

- 2 years, 5 months ago

How does it help?

- 2 years, 5 months ago

Digit sum of the number is $$300$$. Therefore, it is divisible by 3, since 3 divides 300. But it is not divisible by 9, since 9 does not divide 300. Since the number is divisible by 3 but not 9, it can't be a perfect square/

- 2 years, 5 months ago