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

1 Answer
Mar 10, 2016

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 x14=xn 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: 13.93198141.93198
13.931981.93198=12

The case of n = 14 can be solved by inspection.
Since 24=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 1614=2.
The answer to the n = 14 case is c) 16]