Evaluate using formula :
`(i) (188)^(2) " " (ii) (9.4)^(2) " " (iii) (10.9)^(2)`

Answer

To evaluate the squares of the given numbers using the formulas, we will use the identities for (A + B)² and (A - B)².

### Solution Steps:

**(i) Evaluate (188)²:**
1. **Identify A and B:** We can express 188 as (200 - 12).
- Here, A = 200 and B = 12.

2. **Use the formula for (A - B)²:**
\[ (A - B)² = A² - 2AB + B² \]
Substitute A and B:
\[ (200 - 12)² = 200² - 2 \times 200 \times 12 + 12² \]

3. **Calculate each term:**
- \(200² = 40000\)
- \(2 \times 200 \times 12 = 4800\)
- \(12² = 144\)

4. **Combine the results:**
\[ 188² = 40000 - 4800 + 144 = 35200 + 144 = 35344 \]

**Final answer for (i):** \(188² = 35344\)

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**(ii) Evaluate (9.4)²:**
1. **Identify A and B:** We can express 9.4 as (10 - 0.6).
- Here, A = 10 and B = 0.6.

2. **Use the formula for (A - B)²:**
\[ (A - B)² = A² - 2AB + B² \]
Substitute A and B:
\[ (10 - 0.6)² = 10² - 2 \times 10 \times 0.6 + 0.6² \]

3. **Calculate each term:**
- \(10² = 100\)
- \(2 \times 10 \times 0.6 = 12\)
- \(0.6² = 0.36\)

4. **Combine the results:**
\[ 9.4² = 100 - 12 + 0.36 = 88 + 0.36 = 88.36 \]

**Final answer for (ii):** \(9.4² = 88.36\)

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**(iii) Evaluate (10.9)²:**
1. **Identify A and B:** We can express 10.9 as (10 + 0.9).
- Here, A = 10 and B = 0.9.

2. **Use the formula for (A + B)²:**
\[ (A + B)² = A² + 2AB + B² \]
Substitute A and B:
\[ (10 + 0.9)² = 10² + 2 \times 10 \times 0.9 + 0.9² \]

3. **Calculate each term:**
- \(10² = 100\)
- \(2 \times 10 \times 0.9 = 18\)
- \(0.9² = 0.81\)

4. **Combine the results:**
\[ 10.9² = 100 + 18 + 0.81 = 118 + 0.81 = 118.81 \]

**Final answer for (iii):** \(10.9² = 118.81\)

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### Summary of Answers:
- (i) \(188² = 35344\)
- (ii) \(9.4² = 88.36\)
- (iii) \(10.9² = 118.81\)