Mental Cube Root

If the cube root of 1331 1331 is 11 11 and the cube root of 1728 1728 is 12 12 , what is the cube root of 1442897 1442897 ?

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


The answer is 113.

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2 solutions

Danish Ahmed
Jan 21, 2015

Based on the information given, we can conclude the cube root of 1331000 1331000 is 110 110 and the cube root of 1728000 1728000 is 120 120 . 1442897 1442897 is between these two. Since something ending with a 3 3 is the only thing which gives something ending in a 7 7 when cubed, the answer must be 113 113 .

Kartik Kulkarni
Jan 24, 2015

I have actually posted a note related to this

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