89,992 and 251,000

Question

How many integers between 89,992 and 251,000 are perfect squares?

Answer 1

"A perfect square is a number that can be expressed as the product of two equal integers." -- Math Warehouse

 

The perfect squares between 89992 and 251000 are:

   90000   90601  91204  91809 ...  249001  250000

 

These are the squares (product of two equal integers) of 300  301  302  303  ... 499  500

 

There are (500-300)+1 = 201 of them.

 

Answer 2

Let's use some base numbers to reference.

 

 

300² = 90000   is more than 89,992 and closest to 89,992

 

500² = 250000  is less than 251,000 and closest to 251,000

 

 

If we take the difference between 900000 and 2500000 and add 1 to the result, we get

 

(250000 - 90000) + 1 =

 

160,001

 

 

You should have 160,001 integers that are perfect squares.