Final answer:
To find the exact value, we simplify the expression inside the parenthesis, combine like terms, and then multiply by √14, resulting in the exact value of √98 + 12√7.
Step-by-step explanation:
To find the exact value of the expression √14*(3√7+√32-√28+2√2), we need to simplify each term inside the parenthesis and then multiply by √14. Let's start by simplifying each term.
So, the expression inside the parenthesis becomes 3√7 + 4√2 - 2√7 + 2√2. Now, we combine like terms:
The simplified expression inside the parenthesis is now √7 + 6√2. Finally, we multiply this by √14:
Adding these results together, we find the exact value of the expression is √98 + 12√7.