Question

what is the smallest number by which 2058 may be multiplied so that the product is a perfect cube.

please send with photo and explanation. ​

Answer 1

Answer:

Just find the cube of this number and then the remaining result will be multiplied to get perfect cube

Step-by-step explanation:

Answer 2

Answer:

The smallest number by which 2058  may be multiplied so that the product is a perfect cube = 36

Step-by-step explanation:

Given number is 2058

To find,

The smallest number by which the given number  may be multiplied so that the product is a perfect cube.

Solution:

The prime factorization of 2058 =  2 x 3 x 7 x 7 x 7

= 2 x 3 x 7³

To make the 2058 a perfect cube, the power of each prime factor should  be a multiple of 3

The power of 7 is already a multiple of 3.

To get the smallest multiple, to make 2058 a perfect cube, we should make the power of 2 and 3, the smallest multiple of 3

To make the power of the prime factors 2 and 3 is '3' we have to multiply   the expression with  2² x 3² = 4×9 = 36

∴The smallest number by which 2058  may be multiplied so that the product is a perfect cube = 36

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