Question

A rectangle has a side of $\sqrt[3]{33}\text{unit}$ and $\sqrt[3]{39}\text{unit}.$ Find the area of the rectangle and comment whether it is a surd or not.

• A. It is a surd.
• B. Area is $\sqrt[3]{327}{\text{unit}}^2.$
• C. It is not a surd.
• D. Area is $3{\text{unit}}^2.$

Answer 1

Answer: (B), (C), (D)

Area is $3{\text{unit}}^2.$

Two sides of the rectangle are $\sqrt[3]{33}\text{unit}$ and $\sqrt[3]{39}\text{unit}.$

$\text{Area}=\text{length}\times \text{breadth}$
$=\sqrt[3]{33}\text{unit}\times \sqrt[3]{39}\text{unit}$
$=\sqrt[3]{33\times 9}{\text{unit}}^2$
$=\sqrt[3]{33\times 3\times 3}{\text{unit}}^2$
$=3{\text{unit}}^2$

$3$ is not a surd.
$\therefore$ Area of the rectangle is not a surd.