Question

Find the smallest number by which 2916 should be divided so that the quotient is a perfect cube. Also find the cube root of the quotient


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Answer 1

Step-by-step explanation:

Prime factorising 2916, we get,

2916=2×2×3×3×3×3×3×3

=2

2

×3

6

.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 2 and number of 3's is 6.

So we need to multiply another 2 in the factorization to make 2916 a perfect cube.

Hence, the smallest number by which 2916 must be multiplied to obtain a perfect cube is 2.

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Answer 2

Answer:

the number is 2

the qoutient is 5832

cube root is 18