Simplify square root of 63x^3+9x square root of 112x

$\sqrt{63 x^{3}} + 9 x \sqrt{112 x}$

Step 1

Simplify each term.

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

Factor $9$ out of $63$ .

$\sqrt{9 (7) x^{3}} + 9 x \sqrt{112 x}$

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

$\sqrt{3^{2} \cdot 7 x^{3}} + 9 x \sqrt{112 x}$

Factor out $x^{2}$ .

$\sqrt{3^{2} \cdot 7 (x^{2} x)} + 9 x \sqrt{112 x}$

Move $7$ .

$\sqrt{3^{2} x^{2} \cdot 7 x} + 9 x \sqrt{112 x}$

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

$\sqrt{{(3 x)}^{2} \cdot 7 x} + 9 x \sqrt{112 x}$

Add parentheses.

$\sqrt{{(3 x)}^{2} \cdot (7 x)} + 9 x \sqrt{112 x}$

Pull terms out from under the radical.

$3 x \sqrt{7 x} + 9 x \sqrt{112 x}$

Rewrite $112 x$ as ${(2^{2})}^{2} \cdot (7 x)$ .

Factor $16$ out of $112$ .

$3 x \sqrt{7 x} + 9 x \sqrt{16 (7) x}$

Rewrite $16$ as $4^{2}$ .

$3 x \sqrt{7 x} + 9 x \sqrt{4^{2} \cdot 7 x}$

Rewrite $4$ as $2^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

$3 x \sqrt{7 x} + 9 x (2^{2} \sqrt{7 x})$

Raise $2$ to the power of $2$ .

$3 x \sqrt{7 x} + 9 x (4 \sqrt{7 x})$

Multiply $4$ by $9$ .

$3 x \sqrt{7 x} + 36 x \sqrt{7 x}$

Step 2

Add $3 x \sqrt{7 x}$ and $36 x \sqrt{7 x}$ .

$39 x \sqrt{7 x}$