Simplify -2/3 square root of 63x^3

$- \frac{2}{3} \sqrt{63 x^{3}}$

Step 1

Rewrite $63 x^{3}$ as ${(3 x)}^{2} \cdot (7 x)$ .

Factor $9$ out of $63$ .

$- \frac{2}{3} \cdot \sqrt{9 (7) x^{3}}$

Rewrite $9$ as $3^{2}$ .

$- \frac{2}{3} \cdot \sqrt{3^{2} \cdot 7 x^{3}}$

Factor out $x^{2}$ .

$- \frac{2}{3} \cdot \sqrt{3^{2} \cdot 7 (x^{2} x)}$

Move $7$ .

$- \frac{2}{3} \cdot \sqrt{3^{2} x^{2} \cdot 7 x}$

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

$- \frac{2}{3} \cdot \sqrt{{(3 x)}^{2} \cdot 7 x}$

Add parentheses.

$- \frac{2}{3} \cdot \sqrt{{(3 x)}^{2} \cdot (7 x)}$

Step 2

Pull terms out from under the radical.

$- \frac{2}{3} \cdot (3 x \sqrt{7 x})$

Step 3

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} \cdot (3 x \sqrt{7 x})$

Factor $3$ out of $3 x \sqrt{7 x}$ .

$\frac{- 2}{3} \cdot (3 (x \sqrt{7 x}))$

Cancel the common factor.

$\frac{- 2}{3} \cdot (3 (x \sqrt{7 x}))$

Rewrite the expression.

$- 2 \cdot (x \sqrt{7 x})$

$- 2 x \sqrt{7 x}$