225 (15 squared)
256 (16 squared)
289 (17 squared)
324 (18 squared)
1,4,9,16,25,36,49,64,81,100,121,144,169,196.
There are total 11 perfect squares between 10 to 200, which are 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 :)
Only 15^2 falls between 200 and 250.15^2 = 225.
300
25 < 30 < 36 so that 52 < 30 < 62 196 < 200 < 225 so that 142 < 200 < 152 So the squares of the numbers 6, 7, ... 14 are the required numbers.
1,4,9,16,25,36,49,64,81,100,121,144,169,196.
There are total 11 perfect squares between 10 to 200, which are 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 :)
121 and 196
1166650
Only 15^2 falls between 200 and 250.15^2 = 225.
300
25 < 30 < 36 so that 52 < 30 < 62 196 < 200 < 225 so that 142 < 200 < 152 So the squares of the numbers 6, 7, ... 14 are the required numbers.
Well, isn't that just a happy little riddle! Ralph likes numbers that are perfect squares, like 25, 400, and 144. Since 200 is also a perfect square (200 x 200 = 40,000), that's why Ralph likes it too. Just like painting, sometimes things just fit together perfectly!
The square numbers between 100 and 200 are 121, 144, 169, and 196. These correspond to the squares of integers 11 (11² = 121), 12 (12² = 144), 13 (13² = 169), and 14 (14² = 196).
Two perfect squares greater than 100 and less than 200 are 121 (which is (11^2)) and 144 (which is (12^2)). Another pair is 169 (which is (13^2)) and 196 (which is (14^2)). These values fit the criteria of being perfect squares within the specified range.
Simply calculate the cubes of a few small numbers, and check which of them are in the desired range.
Infinitely many numbers are below 200.