Question

Is the expression $\sqrt[3]{364\times 13}$ a surd?

• A. yes
• B. no

Answer 1

The correct option is A yes

Simplify the expression $\sqrt[3]{364\times 13}$
$\Rightarrow \sqrt[3]{364\times 13}$
$=\sqrt[3]{32\times 2\times 2\times 2\times 2\times 2\times 13}$
$=\sqrt[3]{32^3}\times \sqrt[3]{32^3}\times \sqrt[3]{313}$
$=2\times 2\times \sqrt[3]{313}$
$=4\sqrt[3]{313}$
The simplified expression is $4$ multiplied by an irrational number $\sqrt[3]{313}$, so the resultant number will be an irrational number.
Hence, $\sqrt[3]{364\times 13}$ is a surd.