Simplify - square root of 28x^4+9x square root of 112x^2

$- \sqrt{28 x^{4}} + 9 x \sqrt{112 x^{2}}$

Step 1

Simplify each term.

Rewrite $28 x^{4}$ as ${(2 x^{2})}^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$- \sqrt{4 (7) x^{4}} + 9 x \sqrt{112 x^{2}}$

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

$- \sqrt{2^{2} \cdot 7 x^{4}} + 9 x \sqrt{112 x^{2}}$

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

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

Move $7$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 1$ .

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

Rewrite $112 x^{2}$ as ${(4 x)}^{2} \cdot 7$ .

Factor $16$ out of $112$ .

$- 2 x^{2} \sqrt{7} + 9 x \sqrt{16 (7) x^{2}}$

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

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

Move $7$ .

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

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

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

Pull terms out from under the radical.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $9$ .

$- 2 x^{2} \sqrt{7} + 36 x^{2} \sqrt{7}$

Step 2

Add $- 2 x^{2} \sqrt{7}$ and $36 x^{2} \sqrt{7}$ .

$34 x^{2} \sqrt{7}$