Solve =frac{5sqrt{45}}{3}+frac{3sqrt{80}}{4}-frac{sqrt{245}}{7}+frac{2sqrt{125}}{5}

$$= \frac { 5 \sqrt { 45 } } { 3 } + \frac { 3 \sqrt { 80 } } { 4 } - \frac { \sqrt { 245 } } { 7 } + \frac { 2 \sqrt { 125 } } { 5 }$$

Evaluate

$$9\sqrt{5}\approx 20.124611797$$

Solution Steps

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}.

$$\frac{5\times 3\sqrt{5}}{3}+\frac{3\sqrt{80}}{4}-\frac{\sqrt{245}}{7}+\frac{2\sqrt{125}}{5}$$

Multiply 5 and 3 to get 15.

$$\frac{15\sqrt{5}}{3}+\frac{3\sqrt{80}}{4}-\frac{\sqrt{245}}{7}+\frac{2\sqrt{125}}{5}$$

Divide 15\sqrt{5} by 3 to get 5\sqrt{5}.

$$5\sqrt{5}+\frac{3\sqrt{80}}{4}-\frac{\sqrt{245}}{7}+\frac{2\sqrt{125}}{5}$$

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}.

$$5\sqrt{5}+\frac{3\times 4\sqrt{5}}{4}-\frac{\sqrt{245}}{7}+\frac{2\sqrt{125}}{5}$$

Multiply 3 and 4 to get 12.

$$5\sqrt{5}+\frac{12\sqrt{5}}{4}-\frac{\sqrt{245}}{7}+\frac{2\sqrt{125}}{5}$$

Divide 12\sqrt{5} by 4 to get 3\sqrt{5}.

$$5\sqrt{5}+3\sqrt{5}-\frac{\sqrt{245}}{7}+\frac{2\sqrt{125}}{5}$$

Combine 5\sqrt{5} and 3\sqrt{5} to get 8\sqrt{5}.

$$8\sqrt{5}-\frac{\sqrt{245}}{7}+\frac{2\sqrt{125}}{5}$$

Factor 245=7^{2}\times 5. Rewrite the square root of the product \sqrt{7^{2}\times 5} as the product of square roots \sqrt{7^{2}}\sqrt{5}. Take the square root of 7^{2}.

$$8\sqrt{5}-\frac{7\sqrt{5}}{7}+\frac{2\sqrt{125}}{5}$$

Cancel out 7 and 7.

$$8\sqrt{5}-\sqrt{5}+\frac{2\sqrt{125}}{5}$$

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}.

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

Multiply 2 and 5 to get 10.

$$8\sqrt{5}-\sqrt{5}+\frac{10\sqrt{5}}{5}$$

Divide 10\sqrt{5} by 5 to get 2\sqrt{5}.

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

Combine 8\sqrt{5} and 2\sqrt{5} to get 10\sqrt{5}.

$$10\sqrt{5}-\sqrt{5}$$

Combine 10\sqrt{5} and -\sqrt{5} to get 9\sqrt{5}.

$$9\sqrt{5}$$