Solve 2sqrt{80}-sqrt{45}+sqrt{245}

$$2 \sqrt { 80 } - \sqrt { 45 } + \sqrt { 245 }$$

Evaluate

$$12\sqrt{5}\approx 26.83281573$$

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}.

$$2\times 4\sqrt{5}-\sqrt{45}+\sqrt{245}$$

Multiply 2 and 4 to get 8.

$$8\sqrt{5}-\sqrt{45}+\sqrt{245}$$

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}.

$$8\sqrt{5}-3\sqrt{5}+\sqrt{245}$$

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

$$5\sqrt{5}+\sqrt{245}$$

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}.

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

Combine 5\sqrt{5} and 7\sqrt{5} to get 12\sqrt{5}.

$$12\sqrt{5}$$