Question

write the following in simplified radical form.
\sqrt3{81}

Explanation:

Step1: Factor 81 into perfect cube

$81 = 27 \times 3 = 3^3 \times 3$

Step2: Split the cube root

$\sqrt[3]{3^3 \times 3} = \sqrt[3]{3^3} \times \sqrt[3]{3}$

Step3: Simplify the perfect cube root

$\sqrt[3]{3^3} = 3$

Answer:

$3\sqrt[3]{3}$