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Express
30^((1)/(4)) in simplest radical form.

Express $30^{\frac{1}{4}}$ in simplest radical form.

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Evaluate integers raised to positive rational exponents

Full solution

Q. Express

30^{\frac{1}{4}}

in simplest radical form.

Understand the expression: Understand the expression $30^{(1/4)}$ . $\newline$ The expression $30^{(1/4)}$ means the fourth root of $30$ . The fourth root of a number is the number that, when raised to the power of $4$ , gives the original number.
Determine perfect fourth power: Determine if $30$ can be expressed as a power of a number that is a perfect fourth power. $\newline$ $30$ is not a perfect fourth power, and it cannot be expressed as a power of a number that is a perfect fourth power. However, we can look for factors of $30$ that are perfect fourth powers to simplify the expression.
Factor into prime factors: Factor $30$ into its prime factors. $\newline$ $30 = 2 \times 3 \times 5$ $\newline$ None of these prime factors are perfect fourth powers, so we cannot simplify the expression by extracting a perfect fourth power from under the radical.
Express in simplest form: Express $30^{1/4}$ in simplest radical form. $\newline$ Since we cannot simplify $30$ by extracting a perfect fourth power, the simplest radical form of $30^{1/4}$ is the fourth root of $30$ , which is written as $\sqrt[4]{30}$ with a small $4$ on the radical symbol to indicate the fourth root.

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