Find all the real fourth roots of 0.0001. (Multiple Choice)

Question

a. -0.01 and 0.01
b. -0.1 and 0.1
c. 0.1
d. 0.01

Answer 1

We can write the given problem as

 

⁴ √(1 / 10000)

 

 

According to the rules of radicals,

 

 ⁴ √(1) / ⁴ √(10000)

 

 

If we have an even root, then the value of the root can be both positive and negative.   This is because if we raise a negative value to an even power, the result is positive.  The same goes for positive values.  You probably remember this concept when evaluating square-roots.

 

 

 ± ⁴ √(1)  /  ± ⁴ √(10000) =

 

± 1  / ± 10 =

 

1 / 10  ,    -1 / -10  ,        and     -1 / 10

 

 

So the real fourth roots we can have is

 

-1/10  and  1/10 

 

 

Convert these into decimals,

 

-0.1   and    0.1

 

 

Choose choice (b) as your answer.