Simplify 6x square root of 7x^3+x^2 square root of 63x

$6 x \sqrt{7 x^{3}} + x^{2} \sqrt{63 x}$

Step 1

Simplify each term.

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

Factor out $x^{2}$ .

$6 x \sqrt{7 (x^{2} x)} + x^{2} \sqrt{63 x}$

Reorder $7$ and $x^{2}$ .

$6 x \sqrt{x^{2} \cdot 7 x} + x^{2} \sqrt{63 x}$

Add parentheses.

$6 x \sqrt{x^{2} \cdot (7 x)} + x^{2} \sqrt{63 x}$

Pull terms out from under the radical.

$6 x (x \sqrt{7 x}) + x^{2} \sqrt{63 x}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$6 (x \cdot x) \sqrt{7 x} + x^{2} \sqrt{63 x}$

Multiply $x$ by $x$ .

$6 x^{2} \sqrt{7 x} + x^{2} \sqrt{63 x}$

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

Factor $9$ out of $63$ .

$6 x^{2} \sqrt{7 x} + x^{2} \sqrt{9 (7) x}$

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

$6 x^{2} \sqrt{7 x} + x^{2} \sqrt{3^{2} \cdot 7 x}$

Add parentheses.

$6 x^{2} \sqrt{7 x} + x^{2} \sqrt{3^{2} \cdot (7 x)}$

Pull terms out from under the radical.

$6 x^{2} \sqrt{7 x} + x^{2} (3 \sqrt{7 x})$

Rewrite using the commutative property of multiplication.

$6 x^{2} \sqrt{7 x} + 3 x^{2} \sqrt{7 x}$

Step 2

Add $6 x^{2} \sqrt{7 x}$ and $3 x^{2} \sqrt{7 x}$ .

$9 x^{2} \sqrt{7 x}$