How many perfect squares are there between 200 and1000?
1st perfect square number between 200 and 1000 is 225 = 15 * 15.
And last perfect square number is 961 = 31 * 31.
So:
( 31 - 15 )+ 1 = 16 + 1 = 17
225 = 15 * 15
256 = 16 * 16
289 = 17 * 17
324 = 18 * 18
361 = 19 * 19
400 = 20 * 20
441 = 21 * 21
484 = 22 * 22
529 = 23 * 23
576 = 24 * 24
625 = 25 * 25
676 = 26 * 26
729 = 27 * 27
784 = 28 * 28
841 = 29 * 29
900 = 30 * 30
961 = 31 * 31
14^2 = 196
31^2 = 961
To find the number of perfect squares between 200 and 1000, we need to determine the largest perfect square that is less than or equal to 1000 and the smallest perfect square that is greater than or equal to 200.
First, we find the largest perfect square less than or equal to 1000. We calculate the square root of 1000, which is approximately 31.62. Since we want the largest perfect square, we round down to the nearest whole number, which gives us 31. Therefore, 31^2 = 961 is the largest perfect square less than or equal to 1000.
Next, we find the smallest perfect square greater than or equal to 200. We calculate the square root of 200, which is approximately 14.14. Since we want the smallest perfect square, we round up to the nearest whole number, which gives us 15. Therefore, 15^2 = 225 is the smallest perfect square greater than or equal to 200.
Now, we can determine the number of perfect squares between 200 and 1000 by calculating the difference between the largest and smallest perfect squares:
Number of perfect squares = (Largest perfect square) - (Smallest perfect square) + 1
= 961 - 225 + 1
= 737.
Therefore, there are 737 perfect squares between 200 and 1000.