Solve =frac{8sqrt{5}-8sqrt{2}+sqrt{50}-sqrt{20}}{2}

$$= \frac { 8 \sqrt { 5 } - 8 \sqrt { 2 } + \sqrt { 50 } - \sqrt { 20 } } { 2 }$$

Evaluate

$$\frac{3\sqrt{2}\left(\sqrt{10}-1\right)}{2}\approx 4.586883589$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{8\sqrt{5}-8\sqrt{2}+5\sqrt{2}-\sqrt{20}}{2}$$

Combine -8\sqrt{2} and 5\sqrt{2} to get -3\sqrt{2}.

$$\frac{8\sqrt{5}-3\sqrt{2}-\sqrt{20}}{2}$$

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}.

$$\frac{8\sqrt{5}-3\sqrt{2}-2\sqrt{5}}{2}$$

Combine 8\sqrt{5} and -2\sqrt{5} to get 6\sqrt{5}.

$$\frac{6\sqrt{5}-3\sqrt{2}}{2}$$