# (4 sqrt 3xy^3) (-2 sqrt 6x^3y^2)? Multiply the radical expression

Oct 31, 2017

$- 24 \sqrt{2} {x}^{4} {y}^{5}$

#### Explanation:

$\left(4 \sqrt{3} x {y}^{3}\right) \left(- 2 \sqrt{6} {x}^{3} {y}^{2}\right)$

decomposing each factor:
$\textcolor{w h i t e}{\text{XXX}} = \left(4 \times \sqrt{3} \times x \times {y}^{3}\right) \times \left(\left(- 2\right) \times \sqrt{6} \times {x}^{3} \times {y}^{2}\right)$

regrouping like factors:
$\textcolor{w h i t e}{\text{XXX}} = \left(4 \times \left(- 2\right)\right) \times \left(\sqrt{3} \times \sqrt{6}\right) \times \left(x \times {x}^{3}\right) \times \left({y}^{3} \times {y}^{2}\right)$

combining like factors:
$\textcolor{w h i t e}{\text{XXX}} = \left(- 8\right) \times \left(\sqrt{18}\right) \times \left({x}^{4}\right) \times \left({y}^{5}\right)$

simplifying the $\sqrt{18}$ factor
$\textcolor{w h i t e}{\text{XXX}} = \left(- 8\right) \times \left(3 \sqrt{2}\right) \times \left({x}^{4}\right) \times \left({y}^{5}\right)$

combining the two constant factors
$\textcolor{w h i t e}{\text{XXX}} = \left(- 24 \sqrt{2}\right) \times \left({x}^{4}\right) \times \left({y}^{5}\right)$

back into (compressed) standard form:
$\textcolor{w h i t e}{\text{XXX}} = - 24 \sqrt{2} {x}^{4} {y}^{5}$