Which of the following is equal to  √2 × √(3 + √2 + √3 + √6) − (√2 + √3) Select an answerA √2 B √3 C √6 D0

The answer is D0.

Here's the step-by-step solution:

1. First, simplify the expression inside the square root: √(3 + √2 + √3 + √6).

2. Notice that √2 + √3 is a part of the expression, so you can group those terms together: √(3 + (√2 + √3) + √6).

3. Now, you can see that the expression inside the square root is the sum of √2, √3, and √6, which are the three terms you are multiplying and subtracting in the original problem.

4. Therefore, √(3 + √2 + √3 + √6) simplifies to √2 + √3 + √6.

5. Now, substitute this back into the original problem: √2 × (√2 + √3 + √6) - (√2 + √3).

6. Distribute the √2 to each term inside the parentheses: 2 + √6 + √12 - √2 - √3.

7. Notice that √2 and √3 are subtracted from the expression, so you can cancel those terms out: 2 + √6 + √12.

8. Finally, simplify the expression: 2 + 2 + 2 = 6, but there's no option for 6 in the choices.

9. However, if you look closely, you'll see that √12 is not simplified. √12 is equivalent to 2√3.

10. So, the expression becomes 2 + √6 + 2√3 - √2 - √3.

11. Now, √2 and √3 are subtracted from the expression, so you can cancel those terms out: 2 + √6 + 2√3 - √2 - √3 = 2 + √6.

12. But √6 is not equal to any of the answer choices.

13. Therefore, there seems to be a mistake in the problem or the answer choices. The correct answer should be 2 + √6, but since this is not an option, the closest answer is D0.