Step 1a

The given expression is \$4 \sqrt(12) - 2\sqrt(27) + 5\sqrt(75)\$.

Simplify first radical: \$4\sqrt(12) = 4\sqrt(4 times 3) = 4 times 2 \sqrt(3) = 8\sqrt(3)\$.

Simplify second radical: \$2\sqrt(27) = 2\sqrt(9 times 3) = 2 times 3 \sqrt(3) = 6\sqrt(3)\$.

Simplify third radical: \$5\sqrt(75) = 5\sqrt(25 times 3) = 5 times 5 \sqrt(3) = 25\sqrt(3)\$.

Explanation: Here, the provided radical expressions are simplified individually for clarity and ease of understanding.

Step 1b

Substitute back into the original expression: \$8\sqrt(3) - 6\sqrt(3) + 25\sqrt(3)\$.

Combine like terms: \$ \sqrt(3) ( 8 - 6 + 25)\$.

Simplify the expression: \$27\sqrt(3)\$.

So, therefore the simplified expression is \$27\sqrt(3)\$.

Explanation: Substitute the value into the original expression, combine like terms, and simplify.