Gujarat BoardEnglish MediumSTD 8MATHSSquare Root and Cube-Cube Root1 Mark
Question
The least number by which $72$ be multiplied to make it a perfect cube is __________.
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Answer
The least number by which $72$ be multiplied to make it a perfect cube is $3.$ Solution: Resolving $72$ into prime factors, we get $72 = 2 \times 2 \times 2 \times 3 \times 3$ Grouping the factors in triplets of equal factors, we get $72 = (2 \times 2 \times 2) \times 3 \times 3$ We find that 2 occurs as a prime factor of $72$ thrice, but $3$ occurs as a prime factor only twice. Thus, if we multiply $72$ by $3, 3$ will also occurs as a prime factor thrice and the product will be $2 \times 2 \times 2 \times 3 \times 3 \times 3,$ which is a perfect cube. Hence, the least number, which should be multiplied with $72$ to get perfect cube, is $3.$
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