Find the largest 4-digit number which is a perfect square.
- A9999
- B1899
- C9000
- D9801
Solution & Step-by-step Explanation
The largest 4-digit number is 9999. Let's estimate its square root:
10000
=100
This means the largest 4-digit perfect square must be the square of a number just below 100, which is 99.
Let's calculate 99
2
:
99
2
=(100−1)
2
=10000−200+1=9801
The square of the next integer, 100
2
=10000, is a 5-digit number. Therefore, 9801 is the largest 4-digit perfect square.
10000
=100
This means the largest 4-digit perfect square must be the square of a number just below 100, which is 99.
Let's calculate 99
2
:
99
2
=(100−1)
2
=10000−200+1=9801
The square of the next integer, 100
2
=10000, is a 5-digit number. Therefore, 9801 is the largest 4-digit perfect square.