Understanding the Problem
To find the number of non-perfect square numbers between the squares of 49 and 50, we first need to calculate the squares of these two numbers.
Calculating the Squares
- The square of 49 is 2401.
- The square of 50 is 2500.
Identifying the Range
Now, we need to find the non-perfect square numbers between 2401 and 2500.
- The range we are interested in is from 2402 to 2499 (since 2401 and 2500 are perfect squares).
Counting the Total Numbers in the Range
- The total numbers from 2402 to 2499 can be calculated as follows:
- Total numbers = 2499 - 2402 + 1 = 98
Identifying Perfect Squares in the Range
Next, we need to determine how many perfect squares exist between 2402 and 2499.
- The perfect squares within our range are:
- 49^2 = 2401 (excluded)
- 50^2 = 2500 (excluded)
- The perfect squares between 2401 and 2500 are 2401, 2404 (49^2 + 3), 2409 (49^2 + 8), 2450 (50^2 - 50), and 2500.
However, the only perfect squares in this specific range are:
- 2401 (just below our range)
- 2500 (just above our range)
Thus, there are no perfect squares between 2402 and 2499.
Calculating Non-Perfect Squares
Since there are no perfect squares between 2402 and 2499:
- The number of non-perfect square numbers = Total numbers - Perfect squares
- Non-perfect square numbers = 98 - 0 = 98
Final Answer
Therefore, the total number of non-perfect square numbers between the squares of 49 and 50 is 98.