How many positive integers n with \(n\le 500\) have square roots that can be expressed in the form a√b where a and b are integers with a\(\ge\)10 ?
+128406 I get this many :
sqrt (n) = a*sqrt(b) with a ≥ 10
sqrt (100) = 10sqrt (1)
sqrt (200) = 10sqrt(2)
sqrt (300) = 10sqrt (3)
sqrt (400) = 10sqrt (4) or 20sqrt(1)
sqrt (500) = 10sqrt(5)
sqrt (121) = 11sqrt(1)
sqrt (242) = 11sqrt(2)
sqrt(363) = 11sqrt(3)
sqrt (484) = 11sqrt(4) or 22sqrt(1)
sqrt ( 144) = 12sqrt (1)
sqrt (288) = 12sqrt(2)
sqrt (432) = 12 sqrt (3)
sqrt (169) = 13 sqrt (1)
sqrt (338) = 13sqrt(2)
sqrt (196) = 14sqrt(1)
sqrt (392) = 14sqrt (2)
sqrt(225) = 15sqrt (1)
sqrt (450) = 15sqrt(2)
sqrt (256) = 16sqrt(1)
sqrt (289) = 17sqrt (1)
sqrt ( 324) = 18sqrt(1)
sqrt(361) = 19sqrt(1)
sqrt (441) = 21sqrt(1)
