# How do you simplify sqrt(8x^5)* sqrt(10x^3)?

Jun 27, 2018

$\sqrt{8 {x}^{5}} \cdot \sqrt{10 {x}^{3}} = \textcolor{b l u e}{4 \sqrt{5} {x}^{4}}$

#### Explanation:

$\sqrt{8 {x}^{5}} \cdot \sqrt{10 {x}^{3}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{8 \cdot 10 \cdot {x}^{5} \cdot {x}^{3}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{80 \cdot {x}^{8}}$

$\textcolor{w h i t e}{\text{XXX}} = \sqrt{{4}^{2} \cdot 5 \cdot {\left({x}^{4}\right)}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} = 4 \sqrt{5} {x}^{4}$

Jun 27, 2018

$4 \sqrt{5} {x}^{4}$

#### Explanation:

$\sqrt{8 {x}^{5}} \cdot \sqrt{10 {x}^{3}}$

$= \sqrt{8 {x}^{5} \cdot 10 {x}^{3}}$

$= \sqrt{80 {x}^{8}}$

$= \sqrt{{\left(4 {x}^{4}\right)}^{2} \cdot 5}$

$= 4 \sqrt{5} {x}^{4}$ [Ans]

Jun 27, 2018

$4 \sqrt{5} {x}^{4}$

#### Explanation:

$\sqrt{8 {x}^{5}} \cdot \sqrt{10 {x}^{3}}$

$\therefore {8}^{\frac{1}{2}} \cdot {\left({x}^{5}\right)}^{\frac{1}{2}} \cdot {10}^{\frac{1}{2}} \cdot {\left({x}^{3}\right)}^{\frac{1}{2}}$

$\therefore {2}^{\frac{1}{2}} \cdot {2}^{\frac{1}{2}} \cdot {2}^{\frac{1}{2}} \cdot {x}^{\frac{5}{2}} \cdot {2}^{\frac{1}{2}} \cdot {5}^{\frac{1}{2}} \cdot {x}^{\frac{3}{2}}$

$\therefore {2}^{\frac{4}{2}} \cdot {x}^{\frac{8}{2}} \cdot {5}^{\frac{1}{2}}$

$\therefore {2}^{2} \cdot {x}^{4} \cdot \sqrt{5}$

$\therefore 4 \sqrt{5} {x}^{4}$