Solve frac{sqrt{20}+sqrt{5}}{sqrt{5}}-8

$$\frac { \sqrt { 20 } + \sqrt { 5 } } { \sqrt { 5 } } - 8$$

Evaluate

$$-5$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{2\sqrt{5}+\sqrt{5}}{\sqrt{5}}-8$$

Combine 2\sqrt{5} and \sqrt{5} to get 3\sqrt{5}.

$$\frac{3\sqrt{5}}{\sqrt{5}}-8$$

Rationalize the denominator of \frac{3\sqrt{5}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\sqrt{5}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-8$$

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{5}\sqrt{5}}{5}-8$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{3\times 5}{5}-8$$

Multiply 3 and 5 to get 15.

$$\frac{15}{5}-8$$

Divide 15 by 5 to get 3.

$$3-8$$

Subtract 8 from 3 to get -5.

$$-5$$

Factor

$$-5$$