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Mental Cube Root (Posted on 2004-03-10) Difficulty: 2 of 5
If the cube root of 1331 is 11 and the cube root of 1728 is 12, what is the cube root of 1442897?

(Do this one in your head - no writing or calculators allowed!)

See The Solution Submitted by Gamer    
Rating: 2.6667 (9 votes)

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Solution Solution to the Problem Comment 6 of 6 |
The number is greater than 1.331*10^6 but less than 1.728*10^6 and so; the cube root must lie between 111 and 119 inclusively.....(i)

Since the given positive integer is  congruent to 7 when reduced in modulo 10, it follows that the required cube root  must possess the form 3 ( Mod 10).

Consequently, from (i) it now follows that  the required cube root must be 113. 

Edited on September 12, 2007, 11:28 am
  Posted by K Sengupta on 2007-03-09 05:13:08

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