Let’s do this by examples
Is 216 a perfect cube?
Let’s do prime factorization of 216
Thus,
216 = 2 × 2 × 2 × 3 × 3 × 3
Now,
We make groups of 3
Since 2 & 3 occur in triplets.
∴ 216 is a perfect cube.
Cube root of 216 = 2 × 3
= 6
Is 729 a perfect cube?
Doing Prime factorization of 729
We see that
Since 3 occurs in triplets.
∴ 729 is a perfect cube.
Cube root of 729 = 3 × 3
Is 3375 a perfect cube?
Doing Prime factorization of 3375
We see that
Since 3 & 5 occurs in triplets.
∴ 3375 is a perfect cube.
Cube root of 3375 = 3 × 5
= 15
Is 1125 a perfect cube?
Doing Prime factorization of 1125
We see that
Since 3 does not occur in triplets
∴ 1125 is not a perfect cube.
Is 6859 a perfect cube?
Doing Prime factorization of 6859
We see that
Since 19 occurs in triplets.
∴ 6859 is a perfect cube.
Cube root of 6859 = 19
Is 10648 a perfect cube?
Doing Prime factorization of 10648
We see that
Since 2 & 11 occurs in triplets.
∴ 10648 is a perfect cube.
Cube root of 10648 = 2 × 11
= 22
Is 5324 a perfect cube?
Doing Prime factorization of 5324
We see that
Since 2 does not occur in triplets.
∴ 5324 is not a perfect cube.
Is 968 a perfect cube?
Doing Prime factorization of 968
We see that
Since 11 does not occur in triplets.
∴ 968 is not a perfect cube
Is 400 a perfect cube?
Doing Prime factorization of 400
Since 2 & 5 do not occur in triplets.
∴ 400 is not a perfect cube.