Solve sqrt{20}+2sqrt{80}-3sqrt{180}=

$$\sqrt { 20 } + 2 \sqrt { 80 } - 3 \sqrt { 180 } =$$

Evaluate

$$-8\sqrt{5}\approx -17.88854382$$

Solution Steps

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}.

$$2\sqrt{5}+2\sqrt{80}-3\sqrt{180}$$

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}.

$$2\sqrt{5}+2\times 4\sqrt{5}-3\sqrt{180}$$

Multiply 2 and 4 to get 8.

$$2\sqrt{5}+8\sqrt{5}-3\sqrt{180}$$

Combine 2\sqrt{5} and 8\sqrt{5} to get 10\sqrt{5}.

$$10\sqrt{5}-3\sqrt{180}$$

Factor 180=6^{2}\times 5. Rewrite the square root of the product \sqrt{6^{2}\times 5} as the product of square roots \sqrt{6^{2}}\sqrt{5}. Take the square root of 6^{2}.

$$10\sqrt{5}-3\times 6\sqrt{5}$$

Multiply -3 and 6 to get -18.

$$10\sqrt{5}-18\sqrt{5}$$

Combine 10\sqrt{5} and -18\sqrt{5} to get -8\sqrt{5}.

$$-8\sqrt{5}$$