How do you simplify root3 (x^6 y^7)/root3 9?

1 Answer
Roy Ø.
May 10, 2018

root(3)(x^6y^7)/root(3)9 can be written as =(xy)^2root(3)(y/9)

Explanation:

You have the expression root(3)(x^6y^7)/root(3)9
Remember that the cubic root root(3) of something means a number which multiplied with itself three times (z*z*z) gives the number under the root sign.

("multiplied with itself three times" is, of course, not quite precise, but I mean that n is a factor three times, i.e. z*z*z.)

Let's rewrite the expression a little:

root(3)(x^6y^7)/root(3)9 = root(3)((xy)^6y/3^2)
=(xy)^2root(3)(y/3^2)
Or if you will
=(xy)^2root(3)(y/9)
depending on what you prefer.

We may be fooled to think that root(3)9 can be simplified, but it is not a cubic number. If we had had 27=3^3 instead, we would get the nice expression
=(xy)^2/3root(3)(y)

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
1503 views around the world
You can reuse this answer
Creative Commons License