Question

What is the major difference between odd and even kth roots (when k is a natural number) of a number raised into the kth degree? What is the major difference between odd and even kth roots (when k is a natural number) of a number raised into the kth degree? @Mathematics

Answer 1

So we are looking for the solution to:\[\sqrt[k]{x^k}\] When k is even (like the square root), we see the answer is:\[|x|\]the absolute value of x. Examples:\[\sqrt[4]{(-2)^4}=\sqrt[4]{16}=2=|-2|\]

Answer 2

When k is odd, we dont have to take this precaution. the solutions is just x. Example:\[\sqrt[3]{(-3)^3}=\sqrt[3]{-27}=-3\]

Answer 3

Basically, if k is even, kth roots are NOT unique! there are two of them. the positive and negative value. If k is odd, then the answer IS unique.

Answer 4

that helps me out a lot! how do you figure up the numbers to use in your examples? i cant ever get the right numbers to work out in a problem

Answer 5

well this issue only shows itself when you use negative numbers in your examples. if i had used positive numbers, it would look like everything is fine.