Solve a/sqrt{2/2}=2/sqrt{10/10}

$$\frac { a } { \frac { \sqrt { 2 } } { 2 } } = \frac { 2 } { \frac { \sqrt { 10 } } { 10 } }$$

Solve for a

$$a=2\sqrt{5}\approx 4.472135955$$

Steps for Solving Linear Equation

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

$$\frac{a\times 2}{\sqrt{2}}=\frac{2}{\frac{\sqrt{10}}{10}}$$

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

$$\frac{a\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}=\frac{2}{\frac{\sqrt{10}}{10}}$$

The square of \sqrt{2} is 2.

$$\frac{a\times 2\sqrt{2}}{2}=\frac{2}{\frac{\sqrt{10}}{10}}$$

Divide 2 by \frac{\sqrt{10}}{10} by multiplying 2 by the reciprocal of \frac{\sqrt{10}}{10}.

$$\frac{a\times 2\sqrt{2}}{2}=\frac{2\times 10}{\sqrt{10}}$$

Multiply 2 and 10 to get 20.

$$\frac{a\times 2\sqrt{2}}{2}=\frac{20}{\sqrt{10}}$$

Rationalize the denominator of \frac{20}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{a\times 2\sqrt{2}}{2}=\frac{20\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{a\times 2\sqrt{2}}{2}=\frac{20\sqrt{10}}{10}$$

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

$$\frac{a\times 2\sqrt{2}}{2}=2\sqrt{10}$$

Cancel out 2 and 2.

$$a\sqrt{2}=2\sqrt{10}$$

The equation is in standard form.

$$\sqrt{2}a=2\sqrt{10}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}a}{\sqrt{2}}=\frac{2\sqrt{10}}{\sqrt{2}}$$

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

$$a=\frac{2\sqrt{10}}{\sqrt{2}}$$

Divide 2\sqrt{10} by \sqrt{2}.

$$a=2\sqrt{5}$$