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

Understand the expression: Understand the expression 30^(1/4). 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. 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. 30 = 2 * 3 * 5 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. 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 √(30) with a small 4 on the radical symbol to indicate the fourth root.

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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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Math Problems

Algebra 1

Evaluate integers raised to positive rational exponents

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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.