Open Cubic Root

Mental Trick

It was discovered by the Martial Art writer Liang Yusheng 武侠小说家 梁羽生 (《白发魔女传》作者), who met Hua Luogeng (华罗庚) @1979 in England:
2³= [8]
8³= 51[2]
3³= 2[7]
7³= 34[3]

The last digit pairs :
[2 <->8] , [3 <-> 7]
Others unchanged.

Example:

\sqrt[3]{658503} = N
Last three digits 503 <-> …[7]
First three digits 658:
 (8³ =512)< 658 < (729 = 9³)
=>  8
Answer : \sqrt[3]{658503} = N= 87
Note: Similar trick for opening \sqrt[23] {200 digits} by an indian lady Ms Shakuntala (83) dubbed “Human computer”.

Indian Lady Shakuntala

Human computer