Maths / Cube and Cube Roots / Cube Root by Prime Factorisation

QUESTION

The volume of a cubical box is 32.768 cubic metres. Find the length of a side of the box.

EXPLANATION
Explain TypeExplanation Content
Text

Let the side of cubical box be 'a' metre. The volume of cubical box is $a^3$  cubic metre.

$\therefore \: \: \: \: a^3=32.768\: \: \Rightarrow \: \: a=\sqrt [3]{32.768}\Rightarrow \: \: a=\sqrt [3]{ \frac {32768}{1000}}$

$32768=(2\times2\times2)\times(2\times2\times2)\times(2\times2\times2)\times(2\times2\times2)\times(2\times2\times2)$

$\therefore \: \: \sqrt [3]{32768}=2\times2\times2\times2\times2=32$

$\therefore \: \: \sqrt [3]{1000}=\sqrt [3]{10\times10\times10}=10$

$\therefore \: \: a=\sqrt [3]{\frac {32768}{1000}}=\frac {\sqrt [3]{32768}}{\sqrt [3]{1000}}=\frac {32}{10}=3.2$

$\therefore$   side of cubical box = 3.2 m.

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