Given: sqrt[3]{4}, sqrt{3}, sqrt[6]{25} and s | vedclass

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(B) To compare the surds,we find the $L.C.M.$ of the indices $(3, 2, 6, 12)$,which is $12$.Convert each surd to an equivalent surd with index $12$:$1.

Vedclass · Accepted Answer

$\sqrt{3}$ and $\sqrt[3]{4}$

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(B) To compare the surds,we find the $L.C.M.$ of the indices $(3, 2, 6, 12)$,which is $12$.Convert each surd to an equivalent surd with index $12$:$1. \sqrt[3]{4} = 4^{1/3} = 4^{4/12} = \sqrt[12]{4^4} = \sqrt[12]{256}$$2. \sqrt{3} = 3^{1/2} = 3^{6/12} = \sqrt[12]{3^6} = \sqrt[12]{729}$$3. \sqrt[6]{25} = 25^{1/6} = 25^{2/12} = \sqrt[12]{25^2} = \sqrt[12]{625}$$4. \sqrt[12]{289} = \sqrt[12]{289}$Comparing the radicands: $729 > 625 > 289 > 256$.Therefore,the greatest value is $\sqrt{3}$ and the least value is $\sqrt[3]{4}$.

Given: $\sqrt[3]{4}, \sqrt{3}, \sqrt[6]{25}$ and $\sqrt[12]{289},$ the greatest and least of them are respectively

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