To solve the equation [tex]\(\square^4 = 100000\)[/tex], we need to determine the value of the unknown variable that, when raised to the 4th power, equals 100000. Let's outline the steps:
1. State the equation:
[tex]\[
\square^4 = 100000.
\][/tex]
2. Introduce a variable:
Let [tex]\( x \)[/tex] denote the unknown. Therefore, we rewrite the equation as:
[tex]\[
x^4 = 100000.
\][/tex]
3. Solve for [tex]\( x \)[/tex] by taking the fourth root of both sides:
[tex]\[
x = \sqrt[4]{100000}.
\][/tex]
4. Simplify the fourth root expression:
In some cases, simplifying a root can involve breaking it down into smaller parts, but for this expression, we need to find the numerical value of [tex]\(\sqrt[4]{100000}\)[/tex].
5. Find the value:
Upon calculating the fourth root of 100000, we find that:
[tex]\[
x = 17.78279410038923.
\][/tex]
Therefore, the solution to the equation [tex]\(\square^4 = 100000\)[/tex] is:
[tex]\[
\boxed{17.78279410038923}.
\][/tex]
