Solve frac{sqrt{20}+sqrt{45}}{sqrt{5}}

$$\frac { \sqrt { 20 } + \sqrt { 45 } } { \sqrt { 5 } }$$

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}.

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

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}.

$$\frac{2\sqrt{5}+3\sqrt{5}}{\sqrt{5}}$$

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

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

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

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

The square of \sqrt{5} is 5.

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

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

$$\frac{5\times 5}{5}$$

Multiply 5 and 5 to get 25.

$$\frac{25}{5}$$

Divide 25 by 5 to get 5.

$$5$$

Factor

$$5$$