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Which of the Following Number is Cube of Negative Integer - 1056 . - Mathematics

Sum

Which of the following number is cube of negative integer - 1056 .

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Solution

In order to check if a negative number is a perfect cube, first check if the corresponding positive integer is a perfect cube. Also, for any positive integer m, -m3 is the cube of - m.

On factorising 1056 into prime factors, we get:

\[1056 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 11\]
On grouping the factors in triples of equal factors, we get:​
\[1056 = \left\{ 2 \times 2 \times 2 \right\} \times 2 \times 2 \times 3 \times 11\]
It is evident that the prime factors of 1056 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 1056 is not a perfect cube. This implies that - 1056 is not a perfect cube as well.
 
 
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APPEARS IN

RD Sharma Class 8 Maths
Chapter 4 Cubes and Cube Roots
Exercise 4.2 | Q 2.2 | Page 13
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