SOLUTION: Why is it NOT necessary for two radical expressions have the same index if they are to be multiplied? Provide your own example including correct answer.

Question 1134898: Why is it NOT necessary for two radical expressions have the same index if they are to be multiplied? Provide your own example including correct answer.
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

One way to look at this is to take two radicals: and , which differing indices.
But we can introduce the of and which is and write
and where the number and is the .
This introduces a radical - th root.
Now we multiply under the :
.
So in the general case we need the of the indices as the radical and then we use the power indices under the common radical.
So it is for radical expressions to have the in order to them.
NUMERICAL EXAMPLE:
and
and
We know the answer is .
But let's see if we get the same result by putting and in the formula above.

=
=
=
So the formula works.

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