Solve for x x square root of 2 = square root of 288

$x \sqrt{2} = \sqrt{288}$

Divide each term in $x \sqrt{2} = \sqrt{288}$ by $\sqrt{2}$ .

$\frac{x \sqrt{2}}{\sqrt{2}} = \frac{\sqrt{288}}{\sqrt{2}}$

Simplify the left side.

Cancel the common factor of $\sqrt{2}$ .

Cancel the common factor.

$\frac{x \sqrt{2}}{\sqrt{2}} = \frac{\sqrt{288}}{\sqrt{2}}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{288}}{\sqrt{2}}$

Simplify the right side.

Combine $\sqrt{288}$ and $\sqrt{2}$ into a single radical.

$x = \sqrt{\frac{288}{2}}$

Simplify the expression.

Divide $288$ by $2$ .

$x = \sqrt{144}$

Rewrite $144$ as $12^{2}$ .

$x = \sqrt{12^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = 12$