Which of the following is TRUE?I. sqrt[3]{11} | vedclass

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(C) To compare the values,we express them with a common root index. The indices are $2, 3,$ and $4$. The least common multiple $(LCM)$ of $2, 3,$ and

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Only $III$

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(C) To compare the values,we express them with a common root index. The indices are $2, 3,$ and $4$. The least common multiple $(LCM)$ of $2, 3,$ and $4$ is $12$.$1$. $\sqrt{7} = 7^{1/2} = 7^{6/12} = \sqrt[12]{7^6} = \sqrt[12]{117649}$$2$. $\sqrt[3]{11} = 11^{1/3} = 11^{4/12} = \sqrt[12]{11^4} = \sqrt[12]{14641}$$3$. $\sqrt[4]{45} = 45^{1/4} = 45^{3/12} = \sqrt[12]{45^3} = \sqrt[12]{91125}$Comparing the values inside the $12^{th}$ root: $117649 > 91125 > 14641$.Therefore,$\sqrt{7} > \sqrt[4]{45} > \sqrt[3]{11}$.This corresponds to statement $III$.

Which of the following is $TRUE$?
$I.$ $\sqrt[3]{11} > \sqrt{7} > \sqrt[4]{45}$
$II.$ $\sqrt{7} > \sqrt[3]{11} > \sqrt[4]{45}$
$III.$ $\sqrt{7} > \sqrt[4]{45} > \sqrt[3]{11}$
$IV.$ $\sqrt[4]{45} > \sqrt{7} > \sqrt[3]{11}$

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Which of the following is $TRUE$?$I.$ $\sqrt[3]{11} > \sqrt{7} > \sqrt[4]{45}$$II.$ $\sqrt{7} > \sqrt[3]{11} > \sqrt[4]{45}$$III.$ $\sqrt{7} > \sqrt[4]{45} > \sqrt[3]{11}$$IV.$ $\sqrt[4]{45} > \sqrt{7} > \sqrt[3]{11}$