Solve a=4r/sqrt{2}

$$a = \frac { 4 r } { \sqrt { 2 } }$$

Solve for a

$$a=2\sqrt{2}r$$

Solution Steps

Rationalize the denominator of \frac{4r}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$a=\frac{4r\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$a=\frac{4r\sqrt{2}}{2}$$

Divide 4r\sqrt{2} by 2 to get 2r\sqrt{2}.

$$a=2r\sqrt{2}$$

Solve for r

$$r=\frac{\sqrt{2}a}{4}$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{4r}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$a=\frac{4r\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$a=\frac{4r\sqrt{2}}{2}$$

Divide 4r\sqrt{2} by 2 to get 2r\sqrt{2}.

$$a=2r\sqrt{2}$$

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

$$2r\sqrt{2}=a$$

The equation is in standard form.

$$2\sqrt{2}r=a$$

Divide both sides by 2\sqrt{2}.

$$\frac{2\sqrt{2}r}{2\sqrt{2}}=\frac{a}{2\sqrt{2}}$$

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

$$r=\frac{a}{2\sqrt{2}}$$

Divide a by 2\sqrt{2}.

$$r=\frac{\sqrt{2}a}{4}$$