Solve 2sqrt{2}+3sqrt{8}+sqrt{80}

$$2 \sqrt{ 2 } +3 \sqrt{ 8 } + \sqrt{ 80 }$$

Evaluate

$$4\left(\sqrt{5}+2\sqrt{2}\right)\approx 20.257980409$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}+3\times 2\sqrt{2}+\sqrt{80}$$

Multiply 3 and 2 to get 6.

$$2\sqrt{2}+6\sqrt{2}+\sqrt{80}$$

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

$$8\sqrt{2}+\sqrt{80}$$

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}.

$$8\sqrt{2}+4\sqrt{5}$$