For each of the following, find the least number that must be subtracted so that the resulting number is a perfect square.
(i) `796`
(ii) `1886`
(iii) `23497`

Answer

To solve the problem of finding the least number that must be subtracted from each given number so that the resulting number is a perfect square, we will follow these steps for each case.

### (i) For 796:

1. **Estimate the square root**:
- The square root of 796 is approximately between 28 and 29 because \(28^2 = 784\) and \(29^2 = 841\).

2. **Find the nearest perfect square**:
- The nearest perfect square less than 796 is \(28^2 = 784\).

3. **Calculate the difference**:
- Subtract 784 from 796:
\[ 796 - 784 = 12 \]

4. **Conclusion**:
- The least number that must be subtracted from 796 to make it a perfect square is **12**.

### (ii) For 1886:

1. **Estimate the square root**:
- The square root of 1886 is approximately between 43 and 44 because \(43^2 = 1849\) and \(44^2 = 1936\).

2. **Find the nearest perfect square**:
- The nearest perfect square less than 1886 is \(43^2 = 1849\).

3. **Calculate the difference**:
- Subtract 1849 from 1886:
\[ 1886 - 1849 = 37 \]

4. **Conclusion**:
- The least number that must be subtracted from 1886 to make it a perfect square is **37**.

### (iii) For 23497:

1. **Estimate the square root**:
- The square root of 23497 is approximately between 153 and 154 because \(153^2 = 23409\) and \(154^2 = 23716\).

2. **Find the nearest perfect square**:
- The nearest perfect square less than 23497 is \(153^2 = 23409\).

3. **Calculate the difference**:
- Subtract 23409 from 23497:
\[ 23497 - 23409 = 88 \]

4. **Conclusion**:
- The least number that must be subtracted from 23497 to make it a perfect square is **88**.

### Summary of Results:
- For 796, subtract **12**.
- For 1886, subtract **37**.
- For 23497, subtract **88**.