Question

How many integers greater than 1 million and less than 4 million are squares of integers?
A) 998
B) 999
C) 1000
D) 1998

Can you help and show me a faster way than listing it out!?

Answer 1

√1000000 = 1000
√4000000 = 2000
any number less than 1000 has a square less than 1 million
any number greater than 2000 has a square greater than 4 illion

so, you want all the numbers n such that

1000 < n < 2000