To determine how many numbers lie between the squares of 25 and 26, let's break down the problem with a step-by-step approach:
1. Calculate the square of 25.
[tex]\[
25^2 = 625
\][/tex]
2. Calculate the square of 26.
[tex]\[
26^2 = 676
\][/tex]
3. Find the numbers that lie between these two squares. We are interested in the numbers between 625 and 676, not including the endpoints.
The numbers between 625 and 676 are:
[tex]\[
626, 627, 628, \ldots, 675
\][/tex]
4. Count these numbers to determine how many numbers there are.
To count the numbers from 626 to 675 inclusive, we subtract 625 from 676 and then subtract 1 more to exclude the endpoints:
[tex]\[
676 - 625 - 1 = 50
\][/tex]
Therefore, 50 numbers lie between the squares of 25 and 26.
The correct answer is:
b. 50
