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=(2times2times2)times(2times2times2)times(2times2times2)times(2times2times2)times(2times2times2)

therefore : : sqrt [3]{32768}=2times2times2times2times2=32

therefore : : sqrt [3]{1000}=sqrt [3]{10times10times10}=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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