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

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 ${x}^{\frac{1}{4}} = x - n$ 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: ${13.93198}^{\frac{1}{4}} \cong 1.93198$
$13.93198 - 1.93198 = 12$

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]