Question

How many positive integers with n less than or equal to 500 have square roots that can be expressed in the form a√b where a and b are integers, and n is greater than or equal to 10, and b is as small as possible?

Answer 1

Explanation:

We can solve this problem by finding all the perfect squares with square roots that can be expressed in the form a√b, where a and b are integers, and n is greater than or equal to 10, and b is as small as possible.

The first few perfect squares with roots that can be expressed in this form are:

10^2 = 100 = 10√1

13^2 = 169 = 13√1

17^2 = 289 = 17√1

19^2 = 361 = 19√1

23^2 = 529 = 23√1

There are 5 perfect squares in the range n <= 500 with roots that can be expressed in the form a√b. So, the answer is 5.