Identify the cube root: Identify the cube root of 125. Cube root of 125 is written as root(3)(125). We need to find a number that, when multiplied by itself three times, gives 125.Find the prime factors: Find the prime factors of 125. Prime factors of 125 are 5 × 5 × 5, since 125 = 5^3.Simplify the cube root: Simplify the cube root using the prime factors. root(3)(125) is the same as root(3)(5^3). Since the index of the root (3) matches the exponent of the prime factor (3), the cube root of 5^3 is simply 5.Conclude with the final answer: Conclude with the final answer. Therefore, root(3)(125) = 5.

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$\sqrt[3]{125} =$

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Algebra 1

Simplify radical expressions

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\sqrt[3]{125} =

Identify the cube root: Identify the cube root of $125$ . $\newline$ Cube root of $125$ is written as $\sqrt[3]{125}$ . $\newline$ We need to find a number that, when multiplied by itself three times, gives $125$ .
Find the prime factors: Find the prime factors of $125$ . $\newline$ Prime factors of $125$ are $5 \times 5 \times 5$ , since $125 = 5^3$ .
Simplify the cube root: Simplify the cube root using the prime factors. $\sqrt[3]{125}$ is the same as $\sqrt[3]{5^3}$ . Since the index of the root ( $3$ ) matches the exponent of the prime factor ( $3$ ), the cube root of $5^3$ is simply $5$ .
Conclude with the final answer: Conclude with the final answer. $\newline$ Therefore, $\sqrt[3]{125} = 5$ .