Solve 45^circ=x/sqrt{2}

$$45 ^ { \circ } = \frac { x } { \sqrt { 2 } }$$

Solve for x

$$x=45\sqrt{2}\approx 63.639610307$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{x}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$45=\frac{x\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$45=\frac{x\sqrt{2}}{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x\sqrt{2}}{2}=45$$

Multiply both sides by 2.

$$x\sqrt{2}=45\times 2$$

Multiply 45 and 2 to get 90.

$$x\sqrt{2}=90$$

The equation is in standard form.

$$\sqrt{2}x=90$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{90}{\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$x=\frac{90}{\sqrt{2}}$$

Divide 90 by \sqrt{2}.

$$x=45\sqrt{2}$$