The total non-square numbers that lie between the square of 30 and 31 are(a) 59(b) 61(c) 60(d) 62

To find the total number of non-square numbers between the square of 30 and 31, you can calculate the number of non-square numbers between 30^2 and 31^2 (since 30^2 is the square of 30 and 31^2 is the square of 31) and then subtract 2 from the result because 30^2 and 31^2 are both square numbers.

First, calculate 30^2 and 31^2:
30^2 = 900
31^2 = 961

Now, find the non-square numbers between 900 and 961. Non-square numbers are those that are not perfect squares.

To find the total number of non-square numbers in this range, you can subtract the number of perfect squares from the total count of numbers:

Total numbers between 900 and 961 = 961 - 900 + 1 = 62

Now, subtract the perfect squares:
There are two perfect squares in this range: 900 (30^2) and 961 (31^2).

So, the total number of non-square numbers between the square of 30 and 31 is 62 - 2 = 60.

Therefore, the correct answer is (c) 60.