Question

$5\sqrt[3]{33}$ represents the pure surd.

• A. $\sqrt[3]{315}$
• B. $\sqrt[3]{3375}$
• C. $\sqrt[3]{375}$
• D. $\sqrt[3]{345}$

Answer 1

The correct option is B $\sqrt[3]{3375}$

(a) Let us factorize the given surd $\sqrt[3]{315}$ as follows:

$\sqrt[3]{315}=\sqrt[3]{33\times 5}=\sqrt[3]{33}\times \sqrt[3]{35}\ne 5\sqrt[3]{33}$

Therefore, the mixed surd $5\sqrt[3]{33}$ does not represents the pure surd $\sqrt[3]{315}$.

(b) Let us factorize the given surd $\sqrt[3]{3375}$ as follows:

$\sqrt[3]{3375}=\sqrt[3]{33\times 5\times 5\times 5}=\sqrt[3]{33\times 5^3}=5\sqrt[3]{33}$

Therefore, the mixed surd $5\sqrt[3]{33}$ represents the pure surd $\sqrt[3]{3375}$.

(c) Let us factorize the given surd $\sqrt[3]{375}$ as follows:

$\sqrt[3]{375}=\sqrt[3]{33\times 5\times 5}=\sqrt[3]{33\times 5^2}\ne 5\sqrt[3]{33}$

Therefore, the mixed surd $5\sqrt[3]{33}$ does not represents the pure surd $\sqrt[3]{375}$.

(d) Let us factorize the given surd $\sqrt[3]{345}$ as follows:

$\sqrt[3]{345}=\sqrt[3]{33\times 3\times 5}=\sqrt[3]{33^2\times 5}\ne 5\sqrt[3]{33}$

Therefore, the mixed surd $5\sqrt[3]{33}$ does not represents the pure surd $\sqrt[3]{345}$.

Hence, $\sqrt[3]{3375}=5\sqrt[3]{33}$