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प्रश्न
The least number by which 72 be multiplied to make it a perfect cube is ______.
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उत्तर
The least number by which 72 be multiplied to make it a perfect cube is 3.
Explanation:
Resolving 72 into prime factors, we get
72 = 2 × 2 × 2 × 3 × 3
Grouping the factors in triplets of equal factors, we get
72 = (2 × 2 × 2) × 3 × 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 × 2 × 2 × 3 × 3 × 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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संबंधित प्रश्न
Find the cube root of the following number by the prime factorisation method.
91125
Using the method of successive subtraction examine whether or not the following numbers is perfect cube 1331 .
\[\sqrt[3]{. . .} = \sqrt[3]{4} \times \sqrt[3]{5} \times \sqrt[3]{6}\]
\[\sqrt[3]{\frac{729}{1331}} = \frac{9}{. . .}\]
Evaluate:
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