SOLUTION: What is the best way to find factors to reduce a radical? Example: cube root of 81.
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Question 433233: What is the best way to find factors to reduce a radical? Example: cube root of 81.
Answer by solver91311(24713) (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
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