Question

Find the least number that must be multiplied 4000 so as to get perfect cube Also find The cube root of the perfect cube

Answer 1

Answer:

2, 20

Step-by-step explanation:

Find the smallest number which when multiplied with 4000 will make the products perfect cube. Also find the cube root of the product

4000 = 2 * 2 *  2  *  2  *  2  *  5 * 5 * 5

4000 = 2³ * 2² *  5³

To make it perfect cube we need to multiply it by 2

4000 * 2 = 2³ * 2² *  5³ * 2

=> 8000 = 2³ * 2³ *  5³

=> 8000 = ( 2 * 2 * 5)³

=> 8000 = (20)³

=> ∛8000 = 20

the smallest number which when multiplied with 4000 will make the products perfect cube = 2

cube root of the product = 20

Answer 2

Answer:

25

Step-by-step explanation:

by prime factorization of 4000,

        we found 4000 = 2*2*2*2*2*2*5*5*5*5

2*2*2 makes a cube

2*2*2 makes a second cube

5*5*5 makes the third cube

and we are left with a 5,

     thus multiplying 5 by 25

we can get a perfect cube

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