Question

9. What is the smallest number by which 1600 must be divided so that the quotient is a
perfect cube?
10. Find the smallest number by which 8788 must be divided so that the quotient is a
perfect cube.​

Answer 1

Answer:

9.Firstly we need to factorize the number 1600

After factorization we get,

⇒1600=  2∗2∗2 ∗  2∗2∗2 ∗  5∗5

​ We need to group the expanded numbers in a group of three since it has to be a perfect cube.  

The number 5 does not form a triplet. It contains only two 5  ′ s. Hence the number 5×5=25 has to be divided so that the quotient becomes a perfect cube.

10.Prime factorising 8788, we get,

8788=2×2×13×13×13

        =22 ×133 .

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

Here, number of 2's is 2 and number of 13's is 3.

So we need to divide 22 from the factorization to make 8788 a perfect cube.

Hence, the smallest number by which 8788 must be divided to obtain a perfect cube is 22 =4.

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