Simplify x square root of 63x^2+4 square root of 63x^4

$x \sqrt{63 x^{2}} + 4 \sqrt{63 x^{4}}$

Step 1

Simplify each term.

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

Factor $9$ out of $63$ .

$x \sqrt{9 (7) x^{2}} + 4 \sqrt{63 x^{4}}$

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

$x \sqrt{3^{2} \cdot 7 x^{2}} + 4 \sqrt{63 x^{4}}$

Move $7$ .

$x \sqrt{3^{2} x^{2} \cdot 7} + 4 \sqrt{63 x^{4}}$

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

$x \sqrt{{(3 x)}^{2} \cdot 7} + 4 \sqrt{63 x^{4}}$

Pull terms out from under the radical.

$x (3 x \sqrt{7}) + 4 \sqrt{63 x^{4}}$

Rewrite using the commutative property of multiplication.

$3 \sqrt{7} x \cdot x + 4 \sqrt{63 x^{4}}$

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

Move $x$ .

$3 \sqrt{7} (x \cdot x) + 4 \sqrt{63 x^{4}}$

Multiply $x$ by $x$ .

$3 \sqrt{7} x^{2} + 4 \sqrt{63 x^{4}}$

Rewrite $63 x^{4}$ as ${(3 x^{2})}^{2} \cdot 7$ .

Factor $9$ out of $63$ .

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

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

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

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Move $7$ .

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

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

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

Pull terms out from under the radical.

$3 \sqrt{7} x^{2} + 4 (3 x^{2} \sqrt{7})$

Multiply $3$ by $4$ .

$3 \sqrt{7} x^{2} + 12 x^{2} \sqrt{7}$

Step 2

Simplify by adding terms.

Reorder the factors of $3 \sqrt{7} x^{2}$ .

$3 x^{2} \sqrt{7} + 12 x^{2} \sqrt{7}$

Add $3 x^{2} \sqrt{7}$ and $12 x^{2} \sqrt{7}$ .

$15 x^{2} \sqrt{7}$