Solve 2sqrt{20}-3sqrt{200}+5sqrt{27}-sqrt{1000}=

$$2 \sqrt { 20 } - 3 \sqrt { 200 } + 5 \sqrt { 27 } - \sqrt { 1000 } =$$

Evaluate

$$4\sqrt{5}+15\sqrt{3}-10\sqrt{10}-30\sqrt{2}\approx -39.124149449$$

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}.

$$2\times 2\sqrt{5}-3\sqrt{200}+5\sqrt{27}-\sqrt{1000}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{5}-3\sqrt{200}+5\sqrt{27}-\sqrt{1000}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$4\sqrt{5}-3\times 10\sqrt{2}+5\sqrt{27}-\sqrt{1000}$$

Multiply -3 and 10 to get -30.

$$4\sqrt{5}-30\sqrt{2}+5\sqrt{27}-\sqrt{1000}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$4\sqrt{5}-30\sqrt{2}+5\times 3\sqrt{3}-\sqrt{1000}$$

Multiply 5 and 3 to get 15.

$$4\sqrt{5}-30\sqrt{2}+15\sqrt{3}-\sqrt{1000}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$4\sqrt{5}-30\sqrt{2}+15\sqrt{3}-10\sqrt{10}$$