Write the fourth root of 162 in simplified radical form

The fourth root of 162 in simplified radical form can be expressed as:

\[
\sqrt[4]{162}
\]

We start by factoring 162:

\[
162 = 2 \times 81 = 2 \times 3^4
\]

Now, rewrite the expression using the factors:

\[
\sqrt[4]{162} = \sqrt[4]{2 \times 3^4}
\]

Since \(\sqrt[4]{3^4} = 3\), we can simplify the radical expression:

\[
\sqrt[4]{162} = 3\sqrt[4]{2}
\]

Thus, the simplified form of the fourth root of 162 is:

\[
3\sqrt[4]{2}
\]

Would you like any further details or have any questions?

Here are 5 related questions:
1. How do you simplify higher-order roots in general?
2. What is the cube root of 162 in simplified form?
3. Can the fourth root of 162 be approximated as a decimal?
4. How would you simplify \(\sqrt[3]{54}\)?
5. How can we express the sixth root of 243 in simplified radical form?

**Tip:** When simplifying roots, always look for the largest perfect power factor to simplify efficiently.

Learn how to simplify the fourth root of 162 using prime factorization and properties of radicals. This step-by-step guide walks through the process, from breaking down 162 to simplifying the radical expression as 3√⁴2. Suitable for students in Grades 9-11.

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