Use a calculator to find a decimal approximation of the following root. $\sqrt[4]{78} \approx$ \[ \sqrt[4]{78} \] (Round to the nearest thousandth.)

Step 1 ：We need to find the fourth root of 78.

Step 2 ：Use a calculator to find a decimal approximation of the following root. \(\sqrt[4]{78}\)

Step 3 ：The decimal approximation of the fourth root of 78 is approximately 2.9718278662008415.

Step 4 ：Round this number to the nearest thousandth to get 2.972.

Step 5 ：Final Answer: The decimal approximation of the fourth root of 78, rounded to the nearest thousandth, is \(\boxed{2.972}\).