# 3 Numbers between 1000 and 2000 that are not perfect squares?

### 8 Answers

- 4 weeks ago
Sqrt(1000) is about 31.6.

32^2 is 1024. So any number from 1001 to 1023 will do.

e.g. 1001, 1002, 1003.

Source(s): Brain - cryptogramcornerLv 64 weeks ago
Expanding on the idea of numbers following a perfect square.

If you know some perfect square and it's square root, you can also know

how many non-perfect squares follow it using the following formula

(n+1)^2 = n^2 + 2n + 1

n^2 is a perfect square, and n^2 + 2n + 1 is a perfect square,

the 2n numbers in between are not

so 2^2 = 4 is a perfect square, (2+1)^2 = 2^2 + 2(2) + 1 = 9 is a perfect

square, but 5, 6, 7, and 8 are not.

In the range in question, 32^2 = 1024 is a perfect square. The next 64

numbers starting with 1025 are not

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- roderick_youngLv 74 weeks ago
Choose any 3 numbers that don't end in 0, 1, 4, 5, 6, or 9. Including non-whole numbers, if that's allowed. 1552, 1003, 1897, 1118, 1500.257

If you know a perfect square already in that range, you can choose a few consecutive numbers and be guarranteed that the others are not squares, because squares are spaced out as you get into bigger numbers. For example, if I knew that 40^2 = 1600 was a perfect square, I could say that 1601, 1602, and 1603 were not perfect squares. Eventually I would hit another perfect square, that of 41, but that would take a while. I leave it as an exercise to you to figure out how far you could count before hitting the next perfect square.

- MorningfoxLv 74 weeks ago
Do you mean whole numbers? Just write down the perfect squares between 1000 and 2000. The pick three numbers that are NOT perfect squares.

Hint: what is 32^2? 44^2?