Let's analyze each number to determine why they cannot be perfect squares:
### (i) 4567
To see why 4567 isn't a perfect square, we can begin with its unit digit:
- The unit digit of 4567 is 7.
- A number ending in 7 cannot be a perfect square because the possible unit digits of perfect squares are 0, 1, 4, 5, 6, and 9. Since 7 is not one of these digits, 4567 cannot be a perfect square.
### (ii) 2453
Next, let's evaluate 2453 by examining its last digit:
- The unit digit of 2453 is 3.
- A number ending in 3 cannot be a perfect square for the same reason as above: the unit digits of perfect squares are 0, 1, 4, 5, 6, and 9. As 3 is not among these digits, 2453 cannot be a perfect square.
### (iii) 6298
For the number 6298, we check its final digit:
- The unit digit of 6298 is 8.
- A number ending in 8 cannot be a perfect square because the possible unit digits for perfect squares are 0, 1, 4, 5, 6, and 9, and 8 is not one of them. Therefore, 6298 cannot be a perfect square.
### (iv) 46292
Considering the number 46292, we notice its last digit:
- The unit digit of 46292 is 2.
- A number ending in 2 cannot be a perfect square since the unit digits of perfect squares are always 0, 1, 4, 5, 6, and 9. Consequently, 2 is excluded from these possibilities, so 46292 cannot be a perfect square.
### (v) 64000
Finally, let's examine 64000 with respect to its final digits:
- The last two digits of 64000 are 00.
- While numbers ending in 00 can be perfect squares (e.g., 100, whose square root is 10), 64000 has a more specific issue:
- For a number ending in 00 to be a perfect square, its square root must end in 0.
- The square root of 64000 is approximately 253.976, which is not an integer, confirming that 64000 cannot be a perfect square.
In summary:
- 4567, 2453, 6298, and 46292 can immediately be ruled out as perfect squares due to their unit digits not matching those of perfect squares.
- 64000, although ending in 00, does not have an integer square root, hence it cannot be a perfect square either.
