Question

Match the given problem to the corresponding simplified radical (points) sqrt(54); sqrt(12); sqrt(18); sqrt(45); 2sqrt(3); 3sqrt(2); 3sqrt(5) * 3sqrt(6)

Answer 1

Let's simplify each of the radical expressions provided:

1. **√54**:
- √54 = √(9 * 6) = √9 * √6 = 3√6.

2. **√12**:
- √12 = √(4 * 3) = √4 * √3 = 2√3.

3. **√18**:
- √18 = √(9 * 2) = √9 * √2 = 3√2.

4. **√45**:
- √45 = √(9 * 5) = √9 * √5 = 3√5.

5. **2√3**:
- This is already in simplified form.

6. **3√2**:
- This is already in simplified form.

7. **3√5 * 3√6**:
- (3√5)(3√6) = 9√(5 * 6) = 9√30.

Now, let’s match the given problems to their corresponding simplified radicals:

- **√54** = **3√6**
- **√12** = **2√3**
- **√18** = **3√2**
- **√45** = **3√5**
- **2√3** = **2√3**
- **3√2** = **3√2**
- **3√5 * 3√6** = **9√30** (not listed in your options)

So the matches are:
- **√54** → **3√6**
- **√12** → **2√3**
- **√18** → **3√2**
- **√45** → **3√5**
- **2√3** → **2√3**
- **3√2** → **3√2**
- **3√5 * 3√6** → **9√30** (not listed, but calculated).