Question

fan/medal
Help with simplifying radicals?

Answer 1

\[(135x ^{12}y ^{10})^{\frac{ 1 }{ 3}}\]

Answer 2

That becomes:

\(^3 \! \! \! \! \! \! \sqrt{135x^{12}y^{10}}\)

Answer 3

I'm still kind of confused on where to go from there

Answer 4

135 = 5 * 27 = 5 * 3 * 3 * 3 = 5 * 3^3
\[x ^{12} = x ^{3} * x ^{3} * x ^{3} * x ^{3}\]
\[y ^{10} = y ^{3} * y ^{3} * y\]

substitute these valuess

Answer 5

We can break away 135 from the rest:

\(^3 \! \! \! \! \! \sqrt{135}\) which simplifies to \(3 \cdot~ ^3 \! \! \! \! \! \sqrt{5}\)

Now we can multiply that to the other part:

\(3 \cdot~^3 \! \! \! \! \! \sqrt{5}~~^3 \! \! \! \! \! \! \sqrt{x^{12}y^{10}} \)