What is the nth root?

When a certain number is raised to the power of n and results in \(x\), that number is called the nth root of \(x\).

The nth root of \(x\) can be represented as \(\sqrt[n]{x}\), and can be calculated as follows

\[ \sqrt[n]{x}=x^{\frac{1}{n}} \]

Example

Example 1

Calculate \(\displaystyle \sqrt[2]{16} \) in the positive range.

Solution

\[ \sqrt[2]{16}=16^{\frac{1}{2}}=4 \]

Example 2

Calculate \(\displaystyle \sqrt[3]{27} \) in the positive range.

Solution

\[ \sqrt{3}{27}=27^{\frac{1}{3}}=3 \]