Question

Multiply 6561 by the smallest number so that product is a perfect cube. Also find the cube root of the product.

Answer 1

Prime factorization of,
6561=(3×3×3)×(3×3×3)×(3×3)

Only two 3's in 3rd bracket , if there would be one more 3 then the final number will be a perfect cube.

Therefore 3 is the smallest number that should be multiplied by 6561 to obtain a perfect cube.

Hence required number=6561×3=19683

Prime factorization of,
19683=(3×3×3)×(3×3×3}×(3×3×3)

Therefore,cube root of 19683=3×3×3=27.

Answer 2

Answer:

Ans is 27

Step-by-step explanation:

Prime factorization of,

6561-(3x3x3)*(3*3*3)*(3*3)

Only two 3's in 3rd bracket, if there would be one more 3 then the final number will be a perfect cube.

Therefore 3 is the smallest number that should be multiplied by 6561 to obtain a perfect cube.

Hence required number=6561×3=19683

Prime factorization of, 19683-(3x3x3)x(3×3×3}*(3*3*3)

Therefore,cube root of 19683=3×3×3=27.

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