Question

find the least number by which each of the following numbers should be multiplied to make it a perfect cube. also, find the cube root of the product in each case. (1) 5488 (11) 34992 (ii) 15552 find the least number by which each of the following numbers should be divided to make it a perfect cube. also, find the cube root of each perfect cube. (1) 5184 (11) 5488 (1) 23328​

Answer 1

Answer:

hope it helps you

Step-by-step explanation:

Prime factorising 7803, we get,

7803=3×3×3×17×17

=3

3

×17

2

.

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

Here, number of 3's is 3 and number of 17's is 2.

So we need to multiply another 17 to the factorization to make 7803 a perfect cube.

Hence, the smallest number by which 7803 must be multiplied to obtain a perfect cube is 17.

Answer 2

Answer:

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube. Grouping the prime factors of 81 into triples, we are left with 3. ∴ 81 is not a perfect cube. Thus, the required smallest number is 3.