Solve frac{sqrt{20}+sqrt{125}}{sqrt{5}}+5

$$\frac { \sqrt { 20 } + \sqrt { 125 } } { \sqrt { 5 } } + 5$$

Evaluate

$$12$$

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}.

$$\frac{2\sqrt{5}+\sqrt{125}}{\sqrt{5}}+5$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

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

Combine 2\sqrt{5} and 5\sqrt{5} to get 7\sqrt{5}.

$$\frac{7\sqrt{5}}{\sqrt{5}}+5$$

Rationalize the denominator of \frac{7\sqrt{5}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{7\sqrt{5}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+5$$

The square of \sqrt{5} is 5.

$$\frac{7\sqrt{5}\sqrt{5}}{5}+5$$

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

$$\frac{7\times 5}{5}+5$$

Multiply 7 and 5 to get 35.

$$\frac{35}{5}+5$$

Divide 35 by 5 to get 7.

$$7+5$$

Add 7 and 5 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$