SOLUTION: What is the best way to find factors to reduce a radical? Example: cube root of 81.

Algebra ->  Square-cubic-other-roots -> SOLUTION: What is the best way to find factors to reduce a radical? Example: cube root of 81.      Log On


   

Question 433233: What is the best way to find factors to reduce a radical? Example: cube root of 81.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Do a prime factorization.

Start with 2. 81 is odd, so 2 is not a factor.

Consider 3. The sum of the digits is divisible by 3, so 3 is a factor.

81 divided by 3 is 27

The sum of the digits of 27 is divisible by 3, so 3 is a factor.

27 divided by 3 is 9.

9 is divisible by 3

9 divided by 3 is 3.

Hence, the prime factorization of 81 is 3 times 3 times 3 times 3 times 3.

Since you are taking a cube root, group like factors in threes. You have one group of three 3s. Take three 3s out of the radical and leave one factor of 3 outside of the radical. One factor of 3 remains under the radical.




John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism