Question

Find the smallest whole number by which each of the following numbers must be multiply to obtain a perfect cube :81​

Answer 1

Step-by-step explanation:

A number is a perfect cube only when each factor in the prime factorization is grouped in triples. Using this concept smallest number to be multiplied can be obtained.

(i) 



81=3×3×3––––––––––×381=33×381=3×3×3_×381=33×3

Here, the prime factor 33 is not present as triples.

Hence, we divide by 8181 by 3,3, so that the obtained number becomes a perfect cube.

Thus,

81÷3=27=3381÷3=27=33 is a perfect cube.

Hence the smallest number by which 8181 should be divided to make a perfect cube is 33.

Answer 2

Answer is in the image

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