SOLUTION: why is the answer to cube root of 9 times cubed root of 6 DIVIDED BY 6 root 2 times 6 root 2 = 3?

Question 395152: why is the answer to
cube root of 9 times cubed root of 6
DIVIDED BY
6 root 2 times 6 root 2
= 3?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

First we can use a property of radicals, , to multiply in both the numerator and the denominator:

I left the radicand in the denominator in the form of for reasons that will become clear soon.
Next we use fractional exponents in the denominator to help us simplify further. Using the pattern we can rewrite the denominator as:

We can see that this fraction will reduce to:

Writing this back in radical form we get:

Now our fraction looks like:

Now we can use another property of radicals, to combine the two radicals into one:

which simplifies to:

And since , this cube root becomes a 3!
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