find the smallest number by which 2560 must be multiplied so that the product is a perfect cube
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6
Firstly, we find prime factor.
2560=2 *2*2*2*2*2*2*2*2*5
Here,
On grouping the factor, we find that 5 is left out.
Therefor, 5 must be multiplied so that the product is a perfect cube.
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tatsam:
the answer is wrong
Answered by
26
Given,
Number = 2560
Prime Factorisation of 2560 =
2560 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5
In the above Prime Factorisation the number 2 is paired thrice. But the number 5 is remained single. Hence, we should multiply 5 × 5 to make perfect cube.
Thus, we should 25 to 2560 to make it a perfect cube.
2560 × 25 = 64000
3√64000 = 240.
Therefore, the perfect cube of 64000 is 240.Hence, we should multiply 25 with 2560 to make it perfect cube.
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