allegansveritatem
Full Member
- Joined
- Jan 10, 2018
- Messages
- 962
This is not, strictly speaking, an algebra problem, but it was included in the problems given at the end of a section in my algebra book. I am being asked to simplify.Here is problem or expression or whatever it is:
Here is book solution:
Here is what I did:
I know how to reduce this sort of expression when the exponent of something in the radicand is the same as the index or greater. But...how do you reduce something where the exponent is 2 and the index is 4? Now, I know that this is true because I checked it on a calculator. And I think I found that any time there is an exponent of 2 and an index of 4 you can subtract the lesser from the greater and result will be the new exponent of that element of the radicand. BUT: Try this with and exponent of 2 and an index of 5 and truth will forsake your results.
So, I am asking: How did the author get from the fourth root of 15^2 to the square root of 15?
Here is book solution:
Here is what I did:
I know how to reduce this sort of expression when the exponent of something in the radicand is the same as the index or greater. But...how do you reduce something where the exponent is 2 and the index is 4? Now, I know that this is true because I checked it on a calculator. And I think I found that any time there is an exponent of 2 and an index of 4 you can subtract the lesser from the greater and result will be the new exponent of that element of the radicand. BUT: Try this with and exponent of 2 and an index of 5 and truth will forsake your results.
So, I am asking: How did the author get from the fourth root of 15^2 to the square root of 15?