Give reason to show that none of the numbers given below is a perfect square.
`(i)2162" (ii)6843" (iii)9637" "(iv)6598`

Answer

To determine whether the given numbers are perfect squares, we can analyze the last digits of each number. A perfect square can only end with certain digits. The possible last digits of perfect squares (from squaring numbers 0 through 9) are:

- 0 (from 0²)
- 1 (from 1² and 9²)
- 4 (from 2² and 8²)
- 5 (from 5²)
- 6 (from 4² and 6²)
- 9 (from 3² and 7²)

Now, let's analyze each number step by step:

### Step 1: Analyze the last digit of 2162
- The last digit is **2**.
- Since **2** is not among the possible last digits of perfect squares, **2162 is not a perfect square**.

### Step 2: Analyze the last digit of 6843
- The last digit is **3**.
- Since **3** is not among the possible last digits of perfect squares, **6843 is not a perfect square**.

### Step 3: Analyze the last digit of 9637
- The last digit is **7**.
- Since **7** is not among the possible last digits of perfect squares, **9637 is not a perfect square**.

### Step 4: Analyze the last digit of 6598
- The last digit is **8**.
- Since **8** is not among the possible last digits of perfect squares, **6598 is not a perfect square**.

### Conclusion
None of the numbers 2162, 6843, 9637, and 6598 are perfect squares because their last digits do not match any of the last digits of perfect squares.

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