Solve sqrt{5}(1/sqrt{5}-2)

$$\sqrt { 5 } ( \frac { 1 } { \sqrt { 5 } } - 2 )$$

Evaluate

$$1-2\sqrt{5}\approx -3.472135955$$

Short Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\sqrt{5}\left(\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-2\right)$$

The square of \sqrt{5} is 5.

$$\sqrt{5}\left(\frac{\sqrt{5}}{5}-2\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{5}{5}.

$$\sqrt{5}\left(\frac{\sqrt{5}}{5}-\frac{2\times 5}{5}\right)$$

Since \frac{\sqrt{5}}{5} and \frac{2\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{5}\times \frac{\sqrt{5}-2\times 5}{5}$$

Do the multiplications in \sqrt{5}-2\times 5.

$$\sqrt{5}\times \frac{\sqrt{5}-10}{5}$$

Express \sqrt{5}\times \frac{\sqrt{5}-10}{5} as a single fraction.

$$\frac{\sqrt{5}\left(\sqrt{5}-10\right)}{5}$$

Use the distributive property to multiply \sqrt{5} by \sqrt{5}-10.

$$\frac{\left(\sqrt{5}\right)^{2}-10\sqrt{5}}{5}$$

The square of \sqrt{5} is 5.

$$\frac{5-10\sqrt{5}}{5}$$

Divide each term of 5-10\sqrt{5} by 5 to get 1-2\sqrt{5}.

$$1-2\sqrt{5}$$