The least number among sqrt[3]{4}, sqrt[4]{5} | vedclass

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(D) To compare the numbers, we express them with a common exponent by finding the least common multiple $(LCM)$ of the indices $3$ and $4$, which is $

Vedclass · Accepted Answer

$\sqrt[4]{5}$

Vedclass · Answer

(D) To compare the numbers, we express them with a common exponent by finding the least common multiple $(LCM)$ of the indices $3$ and $4$, which is $12$. The numbers are: $4^{1/3} = (4^4)^{1/12} = 256^{1/12}$ $5^{1/4} = (5^3)^{1/12} = 125^{1/12}$ $7^{1/4} = (7^3)^{1/12} = 343^{1/12}$ $8^{1/3} = (8^4)^{1/12} = 4096^{1/12}$ Comparing the bases $256, 125, 343, 4096$, the smallest value is $125$. Therefore, $125^{1/12} = \sqrt[4]{5}$ is the least number.

The least number among $\sqrt[3]{4}, \sqrt[4]{5}, \sqrt[4]{7}$ and $\sqrt[3]{8}$ is:

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