How do you simplify sqrt(x^3y^9)?

1 Answer
Feb 4, 2015

First of all, use the fact that \sqrt{a\cdot b}=\sqrt{a}\sqrt{b}. So, we have that \sqrt{x^3y^9}=\sqrt{x^3}\sqrt{y^9}

Let's deal with a root at a time: we can write x^3 as x^2\cdot x. So, \sqrt{x^3}=\sqrt{x^2\cdot x}=\sqrt{x^2}\sqrt{x}=x\sqrt{x}.

For the same reasons, we write y^9 as y^2\cdoty^2\cdoty^2\cdoty^2\cdot y. So, we have that \sqrt{y^9}=\sqrt{y^2\cdoty^2\cdoty^2\cdoty^2\cdot y}=\sqrt{y^2}\sqrt{y^2}\sqrt{y^2}\sqrt{y^2}\sqrt{y}, which equals y^4\sqrt{y}.

Putting the two things together, we have that
\sqrt{x^3y^9} = xy^4\sqrt{xy}.