(i) What number exceeds its fourth root by #12#? (ii) What number exceeds its fourth root by #16#?

1 Answer
Mar 10, 2016

Answer:

13.93198 (To 5D) exceeds its fourth root by 12
16 exceeds its fourth root by 14

Explanation:

In general, the solution (x) may be found from the equation #x^(1/4) = x - n# where n is the amount of the difference (In this case 12 or 14)

When n = 12 the equation may be solved by numerical methods (I used Newton/Raphson)
Check: #13.93198^(1/4) ~= 1.93198#
#13.93198 - 1.93198 = 12#

The case of n = 14 can be solved by inspection.
Since #2^4 = 16#

N.B. The following is not relevant to the post restoration answer:
[If the values at a) through d) in the question are supposed to represent possible answers, and #16 - 14 = 2#.
The answer to the n = 14 case is c) 16]