Question

Suggest any shortcut method to calculate the square and cube root. (it must be trustworthy)

Answer 1

you can easily find out cube root.
see for example have a number 125. 
put the factor tree for it.

125 
/     \
5     25/       \
5      5/       \
5      1

now the factors are 5*5*5
pair them up in 3s (only same numbers should be paired)
thus only one group is available having three 5's .
consider them as 1 
we get only one 5.thus the cube root of 125 is 5.

now for more understanding , take 1000
if we put a factor tree we get,
2 *2*2*5*5*5

again pair them in 3's
put one group of 3 numbers as one 
we get (2*2*2) and (5*5*5)
=2*5
=10
10 is the cube root of 1000

hope it helps!!!!