The given expression is:

$\frac{\left( (19 - 5) \cdot 3 - 4 \cdot 8 \right)^2}{(19 + 5) \cdot 3}$

Step-by-step Solution:

1. Simplify the numerator: $(19 - 5) = 14$ $(19 - 5) \cdot 3 = 14 \cdot 3 = 42$ $4 \cdot 8 = 32$ $(19 - 5) \cdot 3 - 4 \cdot 8 = 42 - 32 = 10$ So, the numerator becomes: $(10)^2 = 100$

2. Simplify the denominator: $(19 + 5) = 24$ $(19 + 5) \cdot 3 = 24 \cdot 3 = 72$

3. Final division: $\frac{100}{72} \approx 1.3889$

So, the result of the expression is approximately 1.3889.

Let me know if you would like more details or have any questions!

Additional Questions:

1. How would the result change if a different tolerance value was used?
2. What if the numbers inside the parentheses were modified slightly? How would that affect the final value?
3. Can you simplify expressions involving square roots in the same way as squares?
4. How does the presence of negative signs impact the calculation of such expressions?
5. What is the significance of setting a tolerance value for answers?

Tip:

Always simplify expressions inside parentheses first to avoid confusion with order of operations.