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

Answer

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Answer

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

Steps

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 $\boxed{2.972}$.