Solve (sqrt{40}+sqrt{80}+sqrt{5}

$$( \sqrt { 40 } + \sqrt { 80 } + \sqrt { 5 }$$

Evaluate

$$2\sqrt{10}+5\sqrt{5}\approx 17.504895208$$

Solution Steps

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}.

$$2\sqrt{10}+\sqrt{80}+\sqrt{5}$$

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}.

$$2\sqrt{10}+4\sqrt{5}+\sqrt{5}$$

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

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