Solve frac{a/sqrt{5}}{5}=frac{sqrt{5}}{frac{sqrt{2}}{2}}

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

Solve for a

$$a=25\sqrt{2}\approx 35.355339059$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$\frac{a}{\sqrt{5}}=5\times 2^{\frac{1}{2}}\sqrt{5}$$

Rationalize the denominator of \frac{a}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{a\sqrt{5}}{\left(\sqrt{5}\right)^{2}}=5\times 2^{\frac{1}{2}}\sqrt{5}$$

The square of \sqrt{5} is 5.

$$\frac{a\sqrt{5}}{5}=5\times 2^{\frac{1}{2}}\sqrt{5}$$

Multiply both sides of the equation by 5.

$$a\sqrt{5}=25\times 2^{\frac{1}{2}}\sqrt{5}$$

Reorder the terms.

$$\sqrt{5}a=25\sqrt{2}\sqrt{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\sqrt{5}a=25\sqrt{10}$$

Divide both sides by \sqrt{5}.

$$\frac{\sqrt{5}a}{\sqrt{5}}=\frac{25\sqrt{10}}{\sqrt{5}}$$

Dividing by \sqrt{5} undoes the multiplication by \sqrt{5}.

$$a=\frac{25\sqrt{10}}{\sqrt{5}}$$

Divide 25\sqrt{10} by \sqrt{5}.

$$a=25\sqrt{2}$$