Simplify 7x square root of 98x^2-x^2 square root of 162

$7 x \sqrt{98 x^{2}} - x^{2} \sqrt{162}$

Step 1

Simplify each term.

Rewrite $98 x^{2}$ as ${(7 x)}^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$7 x \sqrt{49 (2) x^{2}} - x^{2} \sqrt{162}$

Rewrite $49$ as $7^{2}$ .

$7 x \sqrt{7^{2} \cdot 2 x^{2}} - x^{2} \sqrt{162}$

Move $2$ .

$7 x \sqrt{7^{2} x^{2} \cdot 2} - x^{2} \sqrt{162}$

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

$7 x \sqrt{{(7 x)}^{2} \cdot 2} - x^{2} \sqrt{162}$

Pull terms out from under the radical.

$7 x (7 x \sqrt{2}) - x^{2} \sqrt{162}$

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

Move $x$ .

$7 (x \cdot x) (7 \sqrt{2}) - x^{2} \sqrt{162}$

Multiply $x$ by $x$ .

$7 x^{2} (7 \sqrt{2}) - x^{2} \sqrt{162}$

Multiply $7$ by $7$ .

$49 x^{2} \sqrt{2} - x^{2} \sqrt{162}$

Rewrite $162$ as $9^{2} \cdot 2$ .

Factor $81$ out of $162$ .

$49 x^{2} \sqrt{2} - x^{2} \sqrt{81 (2)}$

Rewrite $81$ as $9^{2}$ .

$49 x^{2} \sqrt{2} - x^{2} \sqrt{9^{2} \cdot 2}$

Pull terms out from under the radical.

$49 x^{2} \sqrt{2} - x^{2} (9 \sqrt{2})$

Multiply $9$ by $- 1$ .

$49 x^{2} \sqrt{2} - 9 x^{2} \sqrt{2}$

Step 2

Subtract $9 x^{2} \sqrt{2}$ from $49 x^{2} \sqrt{2}$ .

$40 x^{2} \sqrt{2}$