which is a like radical to $sqrt3{54}$ after simplifying?\n$sqrt3{24}$\n$sqrt3{162}$\n$sqrt{128}$\n$sqrt3{128…
which is a like radical to $sqrt3{54}$ after simplifying?\n$sqrt3{24}$\n$sqrt3{162}$\n$sqrt{128}$\n$sqrt3{128}$
Answer
Explanation:
Step1: Simplify $\sqrt[3]{54}$
We factor 54: $54 = 2\times3^3$. Then $\sqrt[3]{54}=\sqrt[3]{2\times3^3}=3\sqrt[3]{2}$.
Step2: Simplify $\sqrt[3]{24}$
Factor 24: $24 = 2^3\times3$, so $\sqrt[3]{24}=\sqrt[3]{2^3\times3}=2\sqrt[3]{3}$.
Step3: Simplify $\sqrt[3]{162}$
Factor 162: $162=2\times3^4 = 2\times3^3\times3$. Then $\sqrt[3]{162}=\sqrt[3]{2\times3^3\times3}= 3\sqrt[3]{6}$.
Step4: Simplify $\sqrt{128}$
Factor 128: $128 = 2^7$. Then $\sqrt{128}=\sqrt{2^7}=8\sqrt{2}$.
Step5: Simplify $\sqrt[3]{128}$
Factor 128: $128 = 2^7=2^6\times2$. Then $\sqrt[3]{128}=\sqrt[3]{2^6\times2}=4\sqrt[3]{2}$.
Answer:
$\sqrt[3]{128}$