# square numbers

• Oct 14th 2008, 07:45 PM
fecoupefe
square numbers
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?
• Oct 14th 2008, 08:03 PM
vincisonfire
31^2 = 961
45^2 = 2025
44-31 = 13 perfect squares between 1000 and 2000
• Oct 14th 2008, 08:10 PM
Soroban
Hello, fecoupefe!

Quote:

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

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

There are 13 square numbers between 1000 and 2000.

• Oct 14th 2008, 08:13 PM
11rdc11
Quote:

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

$\displaystyle \sqrt{1000}~=~31.62277$

$\displaystyle \sqrt{2000}~=~44.721$

so
$\displaystyle 44-31~=~13$