Question

write the following in simplified radical form.
\sqrt3{250}

Explanation:

Step1: Factor 250

We factor 250 into prime factors. $250 = 2\times125 = 2\times5\times25 = 2\times5\times5\times5 = 2\times5^{3}$.

Step2: Simplify the cube root

Using the property of cube roots $\sqrt[3]{ab}=\sqrt[3]{a}\times\sqrt[3]{b}$ (for real numbers \(a,b\)), we have $\sqrt[3]{250}=\sqrt[3]{2\times5^{3}}$.
Since $\sqrt[3]{5^{3}} = 5$, we can rewrite this as $5\sqrt[3]{2}$.

Answer:

\(5\sqrt[3]{2}\)