# How do you combine the expression 5√8x^3-x√50x?

Jan 11, 2018

$5 \sqrt{2 {x}^{3}}$

#### Explanation:

$5 \sqrt{8 {x}^{3}} - x \sqrt{50 x}$

Bring the $x$ on the 2nd term into the square root like so:

$= 5 \sqrt{8 {x}^{3}} - \sqrt{50 x \cdot {x}^{2}} = 5 \sqrt{8 {x}^{3}} - \sqrt{50 {x}^{3}}$

Now rewrite the coefficients in front of the ${x}^{3}$:

$= 5 \sqrt{4 \times 2 {x}^{3}} - \sqrt{25 \times 2 {x}^{3}}$

Bring the square numbers out of the square root:

$5 \times 2 \sqrt{2 {x}^{3}} - 5 \sqrt{2 {x}^{3}}$

$10 \sqrt{2 {x}^{3}} - 5 \sqrt{2 {x}^{3}} = 5 \sqrt{2 {x}^{3}}$