Question

Each radicand is the same variable raised to an odd power.
In words, explain why you would want to multiply the radicands together first and then simplify the product.

Answer 1

very weird question, radicand sort of implies \(\sqrt{}\)
but a variable raised to an odd number (which implies integer) would not use the "radicand" notation....unless I am understanding something wrong.

Answer 2

@dan815 @nincompoop anyone...

Answer 3

That is the radical symbol, radicand is implying that everything inside of it is raised to an odd power. The question is asking to explain in words why you why you would want to multiply the radicands together first and then simplify the product.
@zzr0ck3r

Answer 4

so something like this? \(\sqrt{x^3}*\sqrt{x^7}\)

Answer 5

I think I get it. I did an example for myself like this\[\sqrt{a ^{3}}\sqrt{a ^{5}}\sqrt{a ^{7}}\sqrt{a ^{9}}=\sqrt{a ^{24}}\]That gives you \[(a ^{24})^{\frac{ 1 }{ 2 }}\]When you figure that out you get \[a ^{12}\]That's the reasoning I can see.

Answer 6

^Personally, I believe that's what the first sentence of the problem is implying. @zzr0ck3r

Answer 7

When you multiply that, your exponent is positive, so it's easier to reduce.

Answer 8

That last comment explains this part correct??
"why you would want to multiply the radicands together first and then simplify the product"
@IMStuck

Answer 9

Basically you multiply all the radicands first, which have odd power, add up all those powers together and then finally do a final division by 2 because of the sqrt.
If you simplify by the sqrt first then you have to do it for every single randicand an then multiply all the terms together anyway..

Answer 10

See? It makes perfect sense. If you can make math easier on yourself, that's definitely the way to go!