Question

which is a like radical to $sqrt3{54}$ after simplifying?
$circ$ $sqrt3{24}$
$circ$ $sqrt3{162}$
$circ$ $sqrt{128}$
$circ$ $sqrt3{128}$
done

Explanation:

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

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

Step2: Simplify each option

• $\sqrt[3]{24} = \sqrt[3]{8 \times 3} = 2\sqrt[3]{3}$
• $\sqrt[3]{162} = \sqrt[3]{81 \times 2} = \sqrt[3]{27 \times 3 \times 2} = 3\sqrt[3]{6}$
• $\sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2}$
• $\sqrt[3]{128} = \sqrt[3]{64 \times 2} = 4\sqrt[3]{2}$

Step3: Identify like radical

Like radicals have the same radicand and index. $3\sqrt[3]{2}$ and $4\sqrt[3]{2}$ match.

Answer:

$\boldsymbol{\sqrt[3]{128}}$