Question 467191: Do you think adding and subtracting radicands are similar to adding and subtracting fractions?
Why or why not?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the numbers under the radical sign operate with the same arithmetic rules as the same numbers outside of the radical sign.
the difference is that they are under the radical sign, and so the final answer will be whatever the root indicated by the radical sign.
example:
you have 1/2 + 3/4
you would combine this by putting everything under a common denominator that will make it become 2/4 + 3/4 = 5/4.
whether or not that expression is under a radical sign (making it a radicand) or outside a radical sign, the operations are the same.
the difference is that the answer is still under the radical sign.
example:
you have sqrt(1/2 + 3/4)
that becomes sqrt(5/4) after the arithmetic operations are performed on it.
so the answer to your question is that the arithmetic operations are the same, except, in one case they are performed outside the radical sign, and in the other case, they are performed inside the radical sign.
some terminology.
in the expression square root of (7), the square root symbol is the radical and the 7 is the radicand (the number under the radical symbol)
if you followed the logic above, you'll see that the operations on (1/2 + 3/4) were the same, regardless of whether those numbers were within the radical sign, or outside of it.
if this answers your question, then fine.
if not, then send me a specific problem you are working on where you decided to question whether the operations are the same.
|
|
|
