Question

find the smallest number by which 69120 must be multiplied to obtain a perfect cube also find the cube root of the resultant number​

Answer 1

Answer:

25

120

Step-by-step explanation:

find the smallest number by which 69120 must be multiplied to obtain a perfect cube also find the cube root of the resultant number​

To find the smallest number by which 69120 must be multiplied  to obtain a perfect cube , we will factorise 69120  & separate the perfect cube and make the remaining cube

69120 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2   *  3 *  3 *  3 * 5

=> 69120 = (2 * 2 * 2) * (2 * 2 * 2) * (2 * 2 * 2) * (3 *  3 *  3)  * 5

=>  69120 = 2³ * 2³ * 2³ * 3³  * 5

=>  69120 = (24)³ * 5

To make it perfect cube we need to multiply the number by 5 * 5 = 25

=> 69120 * 25 = (24)³ * 5 * 5 * 5

=>  69120 * 25 = (24)³ * 5³

=>  69120 * 25 = (120)³

Taking cube root

=> ∛69120 * 25  = 120

the smallest number by which 69120 must be multiplied = 25

the cube root of the resultant number​ = 120

Answer 2

Answer:

25 and 120

Step-by-step explanation:

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