Solve 5sqrt{frac{1/5}-2sqrt{45}}{-sqrt{5}}

$$\frac{ 5 \sqrt{ \frac{ 1 }{ 5 } } -2 \sqrt{ 45 } }{ - \sqrt{ 5 } }$$

Evaluate

$$5$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$\frac{5\times \frac{\sqrt{1}}{\sqrt{5}}-2\sqrt{45}}{-\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$\frac{5\times \frac{1}{\sqrt{5}}-2\sqrt{45}}{-\sqrt{5}}$$

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

$$\frac{5\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-2\sqrt{45}}{-\sqrt{5}}$$

The square of \sqrt{5} is 5.

$$\frac{5\times \frac{\sqrt{5}}{5}-2\sqrt{45}}{-\sqrt{5}}$$

Cancel out 5 and 5.

$$\frac{\sqrt{5}-2\sqrt{45}}{-\sqrt{5}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{\sqrt{5}-2\times 3\sqrt{5}}{-\sqrt{5}}$$

Multiply -2 and 3 to get -6.

$$\frac{\sqrt{5}-6\sqrt{5}}{-\sqrt{5}}$$

Combine \sqrt{5} and -6\sqrt{5} to get -5\sqrt{5}.

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

Cancel out \sqrt{5} in both numerator and denominator.

$$\frac{-5}{-1}$$

Fraction \frac{-5}{-1} can be simplified to 5 by removing the negative sign from both the numerator and the denominator.

$$5$$

Factor

$$5$$