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