Simplify: \[ \sqrt{128 d}= \]

Step 1 ：Given the expression \(\sqrt{128 d}\).

Step 2 ：We need to simplify this expression.

Step 3 ：First, we break down the number 128 into its prime factors. The prime factors of 128 are 2*2*2*2*2*2*2.

Step 4 ：Next, we pair up the identical factors. Each pair of 2's under the square root can be simplified to a single 2 outside the square root. Since there are seven 2's, we get three pairs and one left over. This gives us 2*2*2*\(\sqrt{2}\) = 8*\(\sqrt{2}\).

Step 5 ：Finally, we multiply this by the square root of d to get the simplified expression.

Step 6 ：So, the simplified form of \(\sqrt{128 d}\) is \(8\sqrt{2}\sqrt{d}\).