Simplifying the Expression
1. **Identify Like Terms**:
- In the given expression, we have terms with square roots. To simplify the expression, we need to identify like terms.
2. **Simplify Each Term**:
- We will simplify each term separately by rationalizing the denominator and simplifying the square roots.
3. **Simplify 3√3**:
- This term cannot be simplified further as the square root of 3 is already in its simplest form.
4. **Simplify 2√27**:
- √27 can be simplified by breaking it down into its factors:
√27 = √(9 * 3) = 3√3
- Therefore, 2√27 becomes 2 * 3√3 = 6√3
5. **Simplify 7/√3**:
- To rationalize the denominator, we multiply both the numerator and denominator by √3:
(7/√3) * (√3/√3) = 7√3/3
- Therefore, 7/√3 simplifies to 7√3/3
6. **Combine Terms**:
- Now, we can combine the simplified terms:
3√3 + 6√3 + 7√3/3
7. **Final Simplified Expression**:
- Combining the terms, we get:
3√3 + 6√3 + 7√3/3 = 9√3 + 7√3/3
8. **Final Answer**:
- The simplified form of the expression 3√3 + 2√27 + 7/√3 is 9√3 + 7√3/3.