The Cube Root of 991026973
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Another one from YouTube. Let us find the real value of x, such that

  x³=991026973

991026973 is a 9-digit number, so x<1000.
Let us find x usig the formula: 

  (a-b)³=a³-3a²b+3ab²+b³

where a=1000

Then,

  991026973 = 999999999 - 8973026
            = 1000000000 - 8973026 - 1
            = 1000000000 - 8973027
            = 1000³ - 8973027
            = 1000³ - (9999999 - 1026972)
            = 1000³ - 9999999 + 1026972
            = 1000³ - (9×10⁶ + 999999) + 1026972
            = 1000³ - 9×10⁶ - 999999 + 1026972
            = 1000³ - 9×1000² + 1026972 - 999999
            = 1000³ - 3×1000²×3 + 1026972 - 1000000 + 1
            = 1000³ - 3×1000²×3 + 26972 + 1
            = 1000³ - 3×1000²×3 + 26999 - 27 + 1
            = 1000³ - 3×1000²×3 + 27000 - 27
            = 1000³ - 3×1000²×3 + 27×1000 - 27
            = 1000³ - 3×1000²×3 + 3³×1000 - 3³
            = 1000³ - 3×1000²×3 + 3×1000×3² - 3³
            = (1000 - 3)³

Thus, the cube root of 991026973 is

  x = 1000 - 3 = 997