Question

find the smallest natural number by which 2304 should be multiplied so that the product is a perfect cube also. find the number whose cube product so obtained.

Answer 1

Given: The term 2304

To find: Smallest natural number by which 2304 should be multiplied so that the product is a perfect cube.

Solution:

• Now we have given the number 2304.

• So by division, we get:

          2 I 2304

          2 I 1152

          2 I 576

          2 I 288

          2 I 144

          2 I 72

          2 I 36

          2 I 18

          2 I 9

          3 I 3

          3 I 3

             I 1

• So by this, we can find factors as:

            2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3

• So now by multiplying 2 and 3 once we can obtain a perfect cube.

• So it comes out to be: 2304 x 2 x 3 = 13824

• So cube root of 13824 is 24

Answer:

            So 6 should be multiplies to 2304 to make a perfect cube root.

Answer 2

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