Simplifying a radical expression with all variables

[maroonblazer]

Hi,
I have the following problem:

, where n is an integer >2 and variables in the radicand of an even index are non-negative.

I'm able to reduce/simplify the left side of the multiplication to , however I'm struggling with the right-hand side.

Ideas?

[stapel_eliz]

I have the following problem:

, where n is an integer >2 and variables in the radicand of an even index are non-negative.

You refer to "sides", but that is a term used for equations, where there is an "equals" sign and then two sides. However, what you have posted is an expression; that is, there is no "equals" sign.

Are you perhaps referring to the first of the two factors? If so, how are you "reducing" this to ?

Please reply showing your steps, starting with your combination of the two radicals into one (since they have the same index). Thank you!

[maroonblazer]

Ok, holidays are over, back at it...

Thanks for the tip. Here's what I'm doing:



Now I start to get shaky. I add the exponents, right? Which would give:


(since the +2 and -2, when summed, cancel each other out).

Since then the expression above simplifies to:

which simplifies further to:



Do I have that right?

[stapel_eliz]

Now I start to get shaky. I add the exponents, right? Which would give:

Actually, the sum of and is , so the simplification should be:

. . . . .

Since then....

Actually:

. . . . .

...so the previous expression simplifies as . However, since the square is never negative, the absolute-value bars aren't needed, and you end up with your final result.

I make the big deal about the absolute-value bars because you could be given a "simplification" exercise along these lines where the parity (oddness or evenness) of the exponent and / or the radical will matter. Keep an eye out on your next test; it's often a trick question on exams.