Question

State, with reason, which of the following are surds and which are not :

(i) $\sqrt[3]{325}$

(ii) $\sqrt[3]{340}$

Answer 1

$3\sqrt{25}\times 3\sqrt{40}$

$=3\sqrt{5\times 5}\times 3\sqrt{2\times 2\times 2\times 5}$

$=2\sqrt[3]{35\times 5}\times \sqrt[3]{35}$

$=2\sqrt[3]{3-1\times -1\times -1}$

$=-5$

since, it does not remain in root form

so, it is not a surd