Squares of which of the following numbers will have `1`(one) at their unit's place ?
(i) `57` (ii) `81`
(iii) `139`
(iv) `73`
(v) `64`

Answer

To determine which of the given numbers will have a square that ends with the digit `1`, we need to analyze the unit's place of each number and then find the square of that digit.

### Step-by-Step Solution:

1. **Identify the unit's place of each number:**
- (i) 57 → Unit's place is **7**
- (ii) 81 → Unit's place is **1**
- (iii) 139 → Unit's place is **9**
- (iv) 73 → Unit's place is **3**
- (v) 64 → Unit's place is **4**

2. **Calculate the square of the unit's place for each number:**
- For **57**:
- \(7^2 = 49\) → Unit's place is **9**
- For **81**:
- \(1^2 = 1\) → Unit's place is **1**
- For **139**:
- \(9^2 = 81\) → Unit's place is **1**
- For **73**:
- \(3^2 = 9\) → Unit's place is **9**
- For **64**:
- \(4^2 = 16\) → Unit's place is **6**

3. **Determine which squares end with the digit `1`:**
- From the calculations:
- 57 → 9
- 81 → 1
- 139 → 1
- 73 → 9
- 64 → 6
- The numbers whose squares end with `1` are **81** and **139**.

### Conclusion:
The squares of the numbers **81** and **139** will have `1` at their unit's place.

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