Question

A cuboid has dimentions of $\sqrt{7}\text{unit}\times \sqrt[3]{34}\text{unit}\times \sqrt[4]{49}\text{unit}.$ Find the volume of the cuboid.

• A. $\sqrt[3]{34}\times \sqrt{21}$
• B. $\sqrt[3]{34}\times \sqrt{12}$
• C. $\sqrt[3]{34}\times \sqrt{21}{\text{unit}}^3$
• D. $\sqrt[3]{34}\times \sqrt{21}{\text{unit}}^2$

Answer 1

The correct option is C $\sqrt[3]{34}\times \sqrt{21}{\text{unit}}^3$

$\text{Volume of a cuboid}=\text{length}\times \text{breadth}\times \text{height}$

$\therefore \text{Volume of a cuboid}=\sqrt{7}\text{unit}\times \sqrt[3]{34}\text{unit}\times \sqrt[4]{49}\text{unit}$
$=\sqrt[3]{34}\times \sqrt{7}\times \sqrt[4]{43^2}{\text{unit}}^3$
$=\sqrt[3]{34}\times \sqrt{7}\times \sqrt{3}{\text{unit}}^3$
$=\sqrt[3]{34}\times \sqrt{7\times 3}{\text{unit}}^3$
$=\sqrt[3]{34}\times \sqrt{21}{\text{unit}}^3$