Final answer:
To simplify the expression 2√3(3√2-2)÷√2, we multiply 2√3 through the parentheses and then divide each term by √2, resulting in the simplified form 6√3 - 4.
Step-by-step explanation:
We need to simplify the expression 2√3(3√2-2)÷√2. The simplification process involves applying multiplication to the terms inside the parentheses, and then division by √2. We'll handle the square roots and constants step by step.
Firstly, multiply 2√3 by each term inside the parentheses:
- 2√3 × 3√2 = 6√6
- 2√3 × -2 = -4√3
The expression now is 6√6 - 4√3. Now, we'll divide each term by √2.
- (6√6) / √2 = 6√3
- (-4√3) / √2 = -4
Our simplified expression is 6√3 - 4, which is the final answer.