If the numbers sqrt[3]{9}, sqrt[4]{20}, sqrt[ | vedclass

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(D) To compare the numbers $\sqrt[3]{9}, \sqrt[4]{20}, \sqrt[6]{25}$,we express them with a common index (root).The indices are $3, 4,$ and $6$. The l

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$\sqrt[6]{25} < \sqrt[3]{9} < \sqrt[4]{20}$

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(D) To compare the numbers $\sqrt[3]{9}, \sqrt[4]{20}, \sqrt[6]{25}$,we express them with a common index (root).The indices are $3, 4,$ and $6$. The least common multiple $(LCM)$ of $3, 4,$ and $6$ is $12$.$1$. $\sqrt[3]{9} = 9^{1/3} = 9^{4/12} = (9^4)^{1/12} = (6561)^{1/12} = \sqrt[12]{6561}$$2$. $\sqrt[4]{20} = 20^{1/4} = 20^{3/12} = (20^3)^{1/12} = (8000)^{1/12} = \sqrt[12]{8000}$$3$. $\sqrt[6]{25} = 25^{1/6} = 25^{2/12} = (25^2)^{1/12} = (625)^{1/12} = \sqrt[12]{625}$Comparing the values inside the $12^{th}$ roots: $625 Therefore,$\sqrt[12]{625} < \sqrt[12]{6561} < \sqrt[12]{8000}$,which implies $\sqrt[6]{25} < \sqrt[3]{9} < \sqrt[4]{20}$.

If the numbers $\sqrt[3]{9}, \sqrt[4]{20}, \sqrt[6]{25}$ are arranged in ascending order,then the correct arrangement is:

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