Gujarat BoardEnglish MediumSTD 8MATHSCubes and Cube Roots2 Marks
Question
Which of the following are perfect cube$?\ 106480$
✓
Answer
On factorising $106480$ into prime factors, we get $106480 = 2 \times 2 \times 2 \times 2 \times 5 \times 11 \times 11 \times 11$ Group the factors in triples of equal factors as: $106480 = \{2 \times 2 \times 2\} \times 2 \times 5 \times \{11 \times 11 \times 11\}$ It is evident that the prime factors of $106480$ can be grouped into triples of equal factors and no factor is left over. Therefore, $106480$ is a perfect cube.
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