Solve frac{sqrt{80}+sqrt{45}}{sqrt{125}+sqrt{20}}

$$\frac { \sqrt { 80 } + \sqrt { 45 } } { \sqrt { 125 } + \sqrt { 20 } }$$

Evaluate

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Solution Steps

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{4\sqrt{5}+\sqrt{45}}{\sqrt{125}+\sqrt{20}}$$

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}.

$$\frac{4\sqrt{5}+3\sqrt{5}}{\sqrt{125}+\sqrt{20}}$$

Combine 4\sqrt{5} and 3\sqrt{5} to get 7\sqrt{5}.

$$\frac{7\sqrt{5}}{\sqrt{125}+\sqrt{20}}$$

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}.

$$\frac{7\sqrt{5}}{5\sqrt{5}+\sqrt{20}}$$

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}.

$$\frac{7\sqrt{5}}{5\sqrt{5}+2\sqrt{5}}$$

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

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

Cancel out 7\sqrt{5} in both numerator and denominator.

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Factor

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