Answer:
Cube root is denoted by '∛ ' symbol. Example: ∛8 = ∛(2 × 2 × 2) = 2. Since, 8 is a perfect cube number, it is easy to find the cube root of a number.
...
Cubes and Cube Roots List of 1 to 15.
Number Cube(a3) Cube root ∛a
6 216 1.817
7 343 1.913
8 512 2.000
9 729 2.080
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
19683=(3×3×3)×(3×3×3}×(3×3×3)
Therefore,cube root of 19683=3×3×3=27.
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Verified answer
Answer:
Cube root is denoted by '∛ ' symbol. Example: ∛8 = ∛(2 × 2 × 2) = 2. Since, 8 is a perfect cube number, it is easy to find the cube root of a number.
...
Cubes and Cube Roots List of 1 to 15.
Number Cube(a3) Cube root ∛a
6 216 1.817
7 343 1.913
8 512 2.000
9 729 2.080
Answer:
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.