Question

what is the radical part of both $sqrt3{54}$ and $sqrt3{128}$ when the expressions are simplified?
$circ$ $sqrt3{2}$
$circ$ $sqrt{2}$
$circ$ $sqrt3{3}$
$circ$ $2$
done

Explanation:

Step1: Simplify $\sqrt[3]{54}$

Factor 54 into $27 \times 2$, so $\sqrt[3]{54} = \sqrt[3]{27 \times 2} = \sqrt[3]{27} \times \sqrt[3]{2} = 3\sqrt[3]{2}$

Step2: Simplify $\sqrt[3]{128}$

Factor 128 into $64 \times 2$, so $\sqrt[3]{128} = \sqrt[3]{64 \times 2} = \sqrt[3]{64} \times \sqrt[3]{2} = 4\sqrt[3]{2}$

Step3: Identify common radical part

Both simplified expressions have $\sqrt[3]{2}$ as the radical part.

Answer:

$\sqrt[3]{2}$ (Option 1)