Arranging the following in descending order,w | vedclass

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(A) To compare the given numbers,we express them with a common index (root).The numbers are $4^{1/3}, 2^{1/2}, 3^{1/6}, 5^{1/4}$.The denominators of t

Vedclass · Accepted Answer

$\sqrt[3]{4} > \sqrt[4]{5} > \sqrt{2} > \sqrt[6]{3}$

Vedclass · Answer

(A) To compare the given numbers,we express them with a common index (root).The numbers are $4^{1/3}, 2^{1/2}, 3^{1/6}, 5^{1/4}$.The denominators of the exponents are $3, 2, 6, 4$. The $LCM$ of these denominators is $12$.Now,rewrite each number with the exponent $1/12$:$4^{1/3} = 4^{4/12} = (4^4)^{1/12} = 256^{1/12}$$2^{1/2} = 2^{6/12} = (2^6)^{1/12} = 64^{1/12}$$3^{1/6} = 3^{2/12} = (3^2)^{1/12} = 9^{1/12}$$5^{1/4} = 5^{3/12} = (5^3)^{1/12} = 125^{1/12}$Comparing the bases: $256 > 125 > 64 > 9$.Therefore,the descending order is $\sqrt[3]{4} > \sqrt[4]{5} > \sqrt{2} > \sqrt[6]{3}$.

Arranging the following in descending order,we get $\sqrt[3]{4}, \sqrt{2}, \sqrt[6]{3}, \sqrt[4]{5}$.

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