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Which of the following is  perfect cube?  1728 - Mathematics

Sum

Which of the following is  perfect cube? 

1728

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Solution

On factorising 1728 into prime factors, we get:

\[1728 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3\]
Group the factors in triples of equal factors as:
\[1728 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 3 \times 3 \times 3 \right\}\]
It is evident that the prime factors of 1728 can be grouped into triples of equal factors and no factor is left over. Therefore, 1728 is a perfect cube.
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APPEARS IN

RD Sharma Class 8 Maths
Chapter 4 Cubes and Cube Roots
Exercise 4.1 | Q 8.05 | Page 8
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