Questions: Simplify. ∛1000

Solution Steps

To simplify the cube root of 1000, we need to find a number that, when multiplied by itself three times, equals 1000. This involves identifying the prime factors of 1000 and determining the cube root.

To simplify \( \sqrt[3]{1000} \), we start by recognizing that \( 1000 \) can be expressed as \( 10^3 \). Therefore, we can rewrite the expression as: \[ \sqrt[3]{1000} = \sqrt[3]{10^3} \]

Using the property of exponents that states \( \sqrt[n]{a^n} = a \), we can simplify the expression: \[ \sqrt[3]{10^3} = 10 \]

Final Answer