Simplify.
22.0625 – [15 + 0.25 × (4.78 – 1.5 × 3.02)]

To simplify the given expression, we follow the standard order of operations (PEMDAS/BODMAS), which dictates that we perform calculations inside parentheses first, starting from the innermost brackets.

The given expression is:
$22.0625\; -\; [15\; +\; 0.25\; \times \; (4.78\; -\; 1.5\; \times \; 3.02)]$

Step 1: Simplify the expression inside the innermost parentheses first.
Within the parentheses $(4.78\; -\; 1.5\; \times \; 3.02)$, we perform multiplication before subtraction:
$1.5\; \times \; 3.02\; =\; 4.53$

Now, substitute this value back into the parentheses:
$4.78\; -\; 4.53\; =\; 0.25$

Step 2: Substitute the result from Step 1 back into the main expression.
The expression now becomes:
$22.0625\; -\; [15\; +\; 0.25\; \times \; 0.25]$

Step 3: Simplify the expression inside the square brackets.
First, perform the multiplication:
$0.25\; \times \; 0.25\; =\; 0.0625$

Now, add 15 to this result:
$15\; +\; 0.0625\; =\; 15.0625$

Step 4: Perform the final subtraction.
Finally, subtract the value inside the square brackets from 22.0625:
$22.0625\; -\; 15.0625\; =\; 7.0$

Therefore, the simplified value of the expression is 7.0.