Evaluate sixth root of 729

Problem

√(6,729)

Solution

1. Identify the goal, which is to find a number x such that x6=729

2. Factor the number 729 into its prime factors to see if it is a perfect power.

3. Divide 729 by 3 repeatedly:

729=3⋅243

243=3⋅81

81=3⋅27

27=3⋅9

9=3⋅3

4. Count the number of factors of 3 to express the number in exponential form:

729=3

5. Apply the definition of the nth root, where √(n,xn)=x for positive x

√(6,3)=3

Final Answer

√(6,729)=3

Want more problems? Check here!