Solve for x x square root of 2=3 square root of 338

$x \sqrt{2} = 3 \sqrt{338}$

Step 1

Simplify.

Rewrite $338$ as $13^{2} \cdot 2$ .

Factor $169$ out of $338$ .

$x \sqrt{2} = 3 \sqrt{169 (2)}$

Rewrite $169$ as $13^{2}$ .

$x \sqrt{2} = 3 \sqrt{13^{2} \cdot 2}$

Pull terms out from under the radical.

$x \sqrt{2} = 3 (13 \sqrt{2})$

Multiply $13$ by $3$ .

$x \sqrt{2} = 39 \sqrt{2}$

Step 2

Divide each term in $x \sqrt{2} = 39 \sqrt{2}$ by $\sqrt{2}$ and simplify.

Divide each term in $x \sqrt{2} = 39 \sqrt{2}$ by $\sqrt{2}$ .

$\frac{x \sqrt{2}}{\sqrt{2}} = \frac{39 \sqrt{2}}{\sqrt{2}}$

Simplify the left side.

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

Cancel the common factor.

$\frac{x \sqrt{2}}{\sqrt{2}} = \frac{39 \sqrt{2}}{\sqrt{2}}$

Divide $x$ by $1$ .

$x = \frac{39 \sqrt{2}}{\sqrt{2}}$

Simplify the right side.

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

Cancel the common factor.

$x = \frac{39 \sqrt{2}}{\sqrt{2}}$

Divide $39$ by $1$ .

$x = 39$