Increasing Order of Surds

Question

Arrange the following surds in increasing order : (A) $\sqrt[3]{2}$ (B) $\sqrt{3}$ (C) $\sqrt[4]{5}$ (D) $\sqrt[6]{7}$ Choose the correct answer from the options given below :

Accepted Answer

D. Express each surd with a common power of $\frac{1}{12}$: - $A = 2^{1/3} = 2^{4/12} = 16^{1/12}$ - $B = 3^{1/2} = 3^{6/12} = 729^{1/12}$ - $C = 5^{1/4} = 5^{3/12} = 125^{1/12}$ - $D = 7^{1/6} = 7^{2/12} = 49^{1/12}$ Comparing base values: $16 < 49 < 125 < 729 \implies A < D < C < B$.

Answer

A < B < C < D

Answer

D < A < C < B

Answer

D < B < C < A

Answer

A < D < C < B

Increasing Order of Surds

Explanation

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