To find the fourth root of 162, let's break down the steps:
1. Understanding the Problem:
Taking the fourth root of a number means identifying a value that, when raised to the power of 4, equals that number.
2. Expressing Mathematically:
The fourth root of 162 can be expressed as:
[tex]\[
\sqrt[4]{162}
\][/tex]
This expression is equivalent to:
[tex]\[
162^{\frac{1}{4}}
\][/tex]
3. Calculating:
To find [tex]\( 162^{\frac{1}{4}} \)[/tex], we need to determine the number which, when raised to the power of 4, equals 162.
4. Result:
After evaluating, the fourth root of 162 is approximately:
[tex]\[
\sqrt[4]{162} \approx 3.5676213450081633
\][/tex]
So, the final result of [tex]\(\sqrt[4]{162}\)[/tex] is approximately [tex]\(3.5676213450081633\)[/tex].
