What is the negative fourth root of 16?

Question

-⁴√16 (Take note the negative is in front of the root as a whole)

My teacher mentioned following the algebra rule of when the radical is an even number, the answer must always be positive. But what if the root is in negative like the one given above?

What will the answer be? -2? 2?

Answer 1

Hello again Kay,

Maybe this will help you see it,

-⁴√16 = -1⁴√16 = -1(⁴√16)= -1 (+2) = -2

so yes the fourth root evaluates to a positive but the negative in front of the root is not part of the root it is multiplying by the result of the root.

Answer 2

4th root of 16 = (16)^1/4 = the square root of the square root of 16 = (16)^1/2^1/2 = 4^1/2

= square root of 4 = 2

then put a minus sign in front

-2

2x2x2x2 = 16, 2 is the 4th root

-2 is minus the 4th root