Which of the following is true?I. frac{1}{sqr | vedclass

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(C) To compare the fractions,we compare their denominators: $\sqrt[3]{12}$,$\sqrt[4]{29}$,and $\sqrt{5}$.First,express them with a common root index (

Vedclass · Accepted Answer

Only $III$

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(C) To compare the fractions,we compare their denominators: $\sqrt[3]{12}$,$\sqrt[4]{29}$,and $\sqrt{5}$.First,express them with a common root index (the least common multiple of $3, 4, 2$ is $12$):$1. \sqrt[3]{12} = 12^{1/3} = 12^{4/12} = \sqrt[12]{12^4} = \sqrt[12]{20736}$$2. \sqrt[4]{29} = 29^{1/4} = 29^{3/12} = \sqrt[12]{29^3} = \sqrt[12]{24389}$$3. \sqrt{5} = 5^{1/2} = 5^{6/12} = \sqrt[12]{5^6} = \sqrt[12]{15625}$Comparing the values inside the $12^{th}$ root:$15625 Therefore,$\sqrt{5} Since the denominators are in the order $\sqrt{5} $\frac{1}{\sqrt{5}} > \frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt[4]{29}}$.This corresponds to statement $III$.

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