Solve frac{10sqrt{2}}{1/2}=z/sqrt{2/2}

$$\frac { 10 \sqrt { 2 } } { \frac { 1 } { 2 } } = \frac { z } { \frac { \sqrt { 2 } } { 2 } }$$

Solve for z

$$z=20$$

Steps for Solving Linear Equation

Divide 10\sqrt{2} by \frac{1}{2} to get 20\sqrt{2}.

$$20\sqrt{2}=\frac{z}{\frac{\sqrt{2}}{2}}$$

Divide z by \frac{\sqrt{2}}{2} by multiplying z by the reciprocal of \frac{\sqrt{2}}{2}.

$$20\sqrt{2}=\frac{z\times 2}{\sqrt{2}}$$

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

$$20\sqrt{2}=\frac{z\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$20\sqrt{2}=\frac{z\times 2\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$20\sqrt{2}=z\sqrt{2}$$

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

$$z\sqrt{2}=20\sqrt{2}$$

The equation is in standard form.

$$\sqrt{2}z=20\sqrt{2}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}z}{\sqrt{2}}=\frac{20\sqrt{2}}{\sqrt{2}}$$

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

$$z=\frac{20\sqrt{2}}{\sqrt{2}}$$

Divide 20\sqrt{2} by \sqrt{2}.

$$z=20$$