Solve {l}{sqrt{80}-sqrt{20}}{+sqrt{40}}

$$\left. \begin{array} { l } { \sqrt { 80 } - \sqrt { 20 } } \\ { + \sqrt { 40 } } \end{array} \right.$$

Evaluate

$$2\left(\sqrt{5}+\sqrt{10}\right)\approx 10.796691275$$

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}.

$$4\sqrt{5}-\sqrt{20}+\sqrt{40}$$

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}.

$$4\sqrt{5}-2\sqrt{5}+\sqrt{40}$$

Combine 4\sqrt{5} and -2\sqrt{5} to get 2\sqrt{5}.

$$2\sqrt{5}+\sqrt{40}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$2\sqrt{5}+2\sqrt{10}$$