find the cube root of the following integers
1) -1728 2) -2744000
Answers
Given : 1) -1728 2) -2744000
To find : Cube root
Solution:
-1728 = (-1)(1728)
= 2 * 864
= 2 * 2 * 432
= 2 * 2 * 2 * 216
= 2 * 2 * 2 * 2 * 108
= 2 * 2 * 2 * 2 * 2 * 54
= 2 * 2 * 2 * 2 * 2 * 2 * 27
= 2 * 2 * 2 * 2 * 2 * 2 * 3 * 9
= 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3
= 2³ *2³ * 3³
= ( 2 * 2 * 3)³
= 12³
=> ∛1728 = 12
∛-1 = -1
=> ∛-1728 = -12
-2744000 = -1 * 2744 * 1000
∛-1 = -1 ∛1000 = 10
2744 = 2 * 1372
= 2 * 2 * 686
= 2 * 2 * 2 * 343
= 2 * 2 * 2 * 7 * 49
= 2 * 2 * 2 * 7 * 7 * 7
= 2³ * 7³
= 14³
=> ∛2744 = 14
=> ∛ -2744000 = (-1)(14)(10) = - 140
∛ -2744000 = - 140
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