Question

How do you subtract `\root[ 3] { 32x ^ { 3} y ^ { 4} } - 3x y \root [ 3] { 4y }`?

Answer 1

Pull as much as you can outside of the first radical, and then group to find your answer, `-xy\root[3]{4y}`

Explanation:

The first thing to do is simplifying the left-hand set of terms. I treat multiplication radicals as their own sets for simplicity, and then I recombine afterwards:

`\root[3]{32x^3y^4}=\root[3]{32} xx \root[3]{x^3} xx \root[3]{y^4}`

`rArr 2\root[3]{4} xx x xx y\root[3]{y} = 2xy\root[3]{4y}`

Now our equation looks like this:

`2xy\root[3]{4y}-3xy\root[3]{4y}`

Next, we'll group the like factor `xy\root[3]{4y}`:

`2xy\root[3]{4y}-3xy\root[3]{4y}=(xy\root[3]{4y})(2-3)`

Finally, we'll do the simple arithmetic in the right-hand parentheses and we'll be done!

`2-3=-1 rArr (-1)(xy\root[3]{4y}) rArr color(red)(-xy\root[3]{4y}`