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

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(D) To compare the numbers $\sqrt[3]{4}, \sqrt[4]{5}, \sqrt[4]{7}, \sqrt[3]{8}$,we convert them to exponents: $4^{1/3}, 5^{1/4}, 7^{1/4}, 8^{1/3}$.Fin

Vedclass · Accepted Answer

$\sqrt[4]{5}$

Vedclass · Answer

(D) To compare the numbers $\sqrt[3]{4}, \sqrt[4]{5}, \sqrt[4]{7}, \sqrt[3]{8}$,we convert them to exponents: $4^{1/3}, 5^{1/4}, 7^{1/4}, 8^{1/3}$.Find the least common multiple $(LCM)$ of the denominators $3$ and $4$,which is $12$.Raise each number to the power of $12$:$(4^{1/3})^{12} = 4^4 = 256$$(5^{1/4})^{12} = 5^3 = 125$$(7^{1/4})^{12} = 7^3 = 343$$(8^{1/3})^{12} = 8^4 = 4096$Comparing the values $256, 125, 343, 4096$,the smallest value is $125$,which corresponds to $\sqrt[4]{5}$.

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

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