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!)

(In reply to solution by mark hartman)

Mr.Mark
you have pointed out very well
i will go along your lines only but some what diffrently
i would seperate them as 1 442 & 897 and take them as it is
the cube of 1 is 1 so we know the begining no. is 1 and as the last digit is 7 which is complementry to 3 for cubes the lat digit is 3
plz note the complementries
1 1
2 8
3 7
4 4
5 5
6 6
7 3
8 2
9 9

after considering the first and the last digits i look at the cube of 12 1728 which is 1 728 and conclude that the middle term is 1 so the no. is 113 this is sure if it is an integral cube. moreover i cross checked with total theory i added 113 numerically 1+1+3=5 and multiplied it with 5 and another 5 to get 125 1+2+5=8 and the total of 1442897=35=3+5=8

thank you

Posted by Rohan Shah on 2004-03-14 07:02:34