Question

what smallest number should 7803 be multiplied with so that the product becomes a perfect cube
please give me with explanation ​

Answer 1

Answer:

17 is the least number to be multiplied

the prime factors of 7803 are 3×3×3×17×17= 3³×17²

for a number to be a perfect cube each number should appear as a multiple of 3.

for example we know that 27 is a perfect cube because it can be represented as 3×3×3

but 24 is not a perfect cube because the prime factors of 24 are 2×2×2×3. here we notice that the number 2 appears 3 times but not the number 3, therefore the least number to be multiplied is 3×3

so that we get 3 three times

similarly the smallest number to be multiplied to 7083 is 17.

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