square numbers

**fecoupefe** · October 14th 2008, 07:45 PM

When a natural number is multiplied by itself,the result is a square number. Some examples of square numbers are 1,4,9,16 and 25.

How many square numbers are there between 1,000 and 2000?

**vincisonfire** · October 14th 2008, 08:03 PM

31^2 = 961
45^2 = 2025
44-31 = 13 perfect squares between 1000 and 2000

**Soroban** · October 14th 2008, 08:10 PM

Hello, fecoupefe!

When a natural number is multiplied by itself,the result is a square number.
Some examples of square numbers are 1, 4, 9, 16 and 25.

How many square numbers are there between 1,000 and 2000?

Since $\sqrt{1000}\approx 31.62$ and $\sqrt{2000} \approx 44.72$

. . the squares are: . $32^2,\:33^2,\:34^2,\hdots,\:44^2$

There are 13 square numbers between 1000 and 2000.

**11rdc11** · October 14th 2008, 08:13 PM

Originally Posted by fecoupefe

When a natural number is multiplied by itself,the result is a square number. Some examples of square numbers are 1,4,9,16 and 25.

How many square numbers are there between 1,000 and 2000?

There are 13 square numbers between 1000 and 2000.

here is why

$\sqrt{1000}~=~31.62277$

$\sqrt{2000}~=~44.721$

so
$44-31~=~13$

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