# How do you divide sqrt(12x^3y^12)/sqrt(27xy^2)?

##### 2 Answers
Mar 22, 2015

Take one big root to get:

and finally taking the square root:
$= \frac{2}{3} \cdot x {y}^{5}$

Hope it helps!

Mar 22, 2015

There are several good approaches to this question:
The reason I try this is that I see some common factors. Namely $3$, $x$, and ${y}^{2}$

Write it as a single square root, then simplify, the break it up into smaller square roots.
Or simplify both numerator and denominator, then simplify what you can.

$\frac{\sqrt{12 {x}^{3} {y}^{12}}}{\sqrt{27 x {y}^{2}}} = \sqrt{\frac{12 {x}^{3} {y}^{12}}{27 x {y}^{2}}} = \sqrt{\frac{4 {x}^{2} {y}^{10}}{9}} = \frac{2 x {y}^{5}}{3}$

Or:

$\frac{\sqrt{12 {x}^{3} {y}^{12}}}{\sqrt{27 x {y}^{2}}} = \frac{\sqrt{4 \cdot 3 \cdot {x}^{2} \cdot x \cdot {y}^{12}}}{\sqrt{9 \cdot 3 \cdot x \cdot {y}^{2}}} = \frac{2 x {y}^{6} \sqrt{3 x}}{3 y \sqrt{3 x}} = \frac{2 x {y}^{5}}{3}$

(Rationalizing the denominator would work too, eventually.)