Final answer:
The expression \((\√{675} - \√{363})²\) simplifies to \((6\√{3})²\) and further to 108.
Step-by-step explanation:
To compute \((\√{675} - \√{363})²\), we can utilize the identity \(a² - 2ab + b²\) which is the expansion of the square of a binomial \((a - b)²\). Let a be \(\√{675}\) and b be \(\√{363}\).
First, we need to find the square roots: \(\√{675} = 25\√{3} = 25 \times 1.732\), and \(\√{363} = 19\√{3} = 19 \times 1.732\). After simplification, \((25\√{3} - 19\√{3})²\) becomes \((6\√{3})^2\).
Finally, squaring \(6\√{3}\) yields \(6² \times 3 = 36 \times 3 = 108\).
Thus, the result of the given expression is \(108\).