Algebra Examples

$\sqrt{2 x^{2}} - 2 \sqrt{72 x^{2}} - 2 \sqrt{72 x^{2}}$

Simplify each term.

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

$\sqrt{x^{2} \cdot 2} - 2 \sqrt{72 x^{2}} - 2 \sqrt{72 x^{2}}$

Pull terms out from under the radical.

$x \sqrt{2} - 2 \sqrt{72 x^{2}} - 2 \sqrt{72 x^{2}}$

Rewrite $72 x^{2}$ as ${(6 x)}^{2} \cdot 2$ .

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Factor $36$ out of $72$ .

$x \sqrt{2} - 2 \sqrt{36 (2) x^{2}} - 2 \sqrt{72 x^{2}}$

Rewrite $36$ as $6^{2}$ .

$x \sqrt{2} - 2 \sqrt{6^{2} \cdot 2 x^{2}} - 2 \sqrt{72 x^{2}}$

Move $2$ .

$x \sqrt{2} - 2 \sqrt{6^{2} x^{2} \cdot 2} - 2 \sqrt{72 x^{2}}$

Rewrite $6^{2} x^{2}$ as ${(6 x)}^{2}$ .

$x \sqrt{2} - 2 \sqrt{{(6 x)}^{2} \cdot 2} - 2 \sqrt{72 x^{2}}$

Pull terms out from under the radical.

$x \sqrt{2} - 2 (6 x \sqrt{2}) - 2 \sqrt{72 x^{2}}$

Multiply $6$ by $- 2$ .

$x \sqrt{2} - 12 (x \sqrt{2}) - 2 \sqrt{72 x^{2}}$

Rewrite $72 x^{2}$ as ${(6 x)}^{2} \cdot 2$ .

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Factor $36$ out of $72$ .

$x \sqrt{2} - 12 x \sqrt{2} - 2 \sqrt{36 (2) x^{2}}$

Rewrite $36$ as $6^{2}$ .

$x \sqrt{2} - 12 x \sqrt{2} - 2 \sqrt{6^{2} \cdot 2 x^{2}}$

Move $2$ .

$x \sqrt{2} - 12 x \sqrt{2} - 2 \sqrt{6^{2} x^{2} \cdot 2}$

Rewrite $6^{2} x^{2}$ as ${(6 x)}^{2}$ .

$x \sqrt{2} - 12 x \sqrt{2} - 2 \sqrt{{(6 x)}^{2} \cdot 2}$

Pull terms out from under the radical.

$x \sqrt{2} - 12 x \sqrt{2} - 2 (6 x \sqrt{2})$

Multiply $6$ by $- 2$ .

$x \sqrt{2} - 12 x \sqrt{2} - 12 x \sqrt{2}$

Simplify by adding terms.

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Subtract $12 x \sqrt{2}$ from $x \sqrt{2}$ .

$- 11 x \sqrt{2} - 12 x \sqrt{2}$

Subtract $12 x \sqrt{2}$ from $- 11 x \sqrt{2}$ .

$- 23 x \sqrt{2}$