Solve for x x square root of 2 = square root of 14

$x \sqrt{2} = \sqrt{14}$

Step 1

Divide each term in $x \sqrt{2} = \sqrt{14}$ by $\sqrt{2}$ .

$\frac{x \sqrt{2}}{\sqrt{2}} = \frac{\sqrt{14}}{\sqrt{2}}$

Step 2

Simplify the left side.

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

Cancel the common factor.

$\frac{x \sqrt{2}}{\sqrt{2}} = \frac{\sqrt{14}}{\sqrt{2}}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{14}}{\sqrt{2}}$

Step 3

Simplify the right side.

Combine $\sqrt{14}$ and $\sqrt{2}$ into a single radical.

$x = \sqrt{\frac{14}{2}}$

Divide $14$ by $2$ .

$x = \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{7}$

Decimal Form:

$x = 2.64575131 \dots$