write the following in simplified radical form. $sqrt3{54}$

Explanation:

Step1: Prime - factorize 54

Express 54 as a product of prime factors: $54 = 2\times3\times3\times3=2\times3^{3}$.

Step2: Simplify the cube - root

$\sqrt[3]{54}=\sqrt[3]{2\times3^{3}}$. Using the property $\sqrt[3]{ab}=\sqrt[3]{a}\cdot\sqrt[3]{b}$ ($a = 2$, $b = 3^{3}$), we get $\sqrt[3]{2\times3^{3}}=\sqrt[3]{3^{3}}\cdot\sqrt[3]{2}$. Since $\sqrt[3]{3^{3}} = 3$, then $\sqrt[3]{54}=3\sqrt[3]{2}$.

Answer:

$3\sqrt[3]{2}$