Question

Find the smallest number by which 69120 must be multiplied to obtain a perfect cube.

Answer 1

Answer:

.

Step-by-step explanation:

69120

/     \

2     34560

/       \

2      17280

/       \

2      8640

/       \

2      4320

/       \

2      2160

/       \

2      1080

/       \

2      540

/       \

2      270

/       \

2      135

/       \

3      45

/       \

3      15

/       \

3      5

/       \

5      1

ie., 69120 = 2^9 x 3^3 x 5

                 = 4³ x 3³ x 5

=> 5² is the smallest no. to be multiplied to get a perfect cube

ie, 25 to be multiplied

if multiplied, we get 4³ x 3³ x 5³

=> the resultant cube root is 4x5x3 = 60

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