Let's first simplify the expression (√14-3√2)²:
(√14 - 3√2)² = (√14 - 3√2)(√14 - 3√2)Expanding this using FOIL (First, Outer, Inner, Last):= (√14)(√14) - (√14)(3√2) - (3√2)(√14) + (3√2)(3√2)= 14 - 3√28 - 3√28 + 18= 32 - 6√28
Now, add 6√28 to this result:(√14 - 3√2)² + 6√28 = 32 - 6√28 + 6√28= 32
Therefore, the final simplified expression is 32.
Let's first simplify the expression (√14-3√2)²:
(√14 - 3√2)² = (√14 - 3√2)(√14 - 3√2)
Expanding this using FOIL (First, Outer, Inner, Last):
= (√14)(√14) - (√14)(3√2) - (3√2)(√14) + (3√2)(3√2)
= 14 - 3√28 - 3√28 + 18
= 32 - 6√28
Now, add 6√28 to this result:
(√14 - 3√2)² + 6√28 = 32 - 6√28 + 6√28
= 32
Therefore, the final simplified expression is 32.