Solve sqrt[3]{243}-2sqrt{125}-3sqrt{72}+3sqrt{45}+2sqrt[3]{9}-sqrt{20}

$$\sqrt[ 3 ] { 243 } - 2 \sqrt { 125 } - 3 \sqrt { 72 } + 3 \sqrt { 45 } + 2 \sqrt[ 3 ] { 9 } - \sqrt { 20 }$$

Evaluate

$$5\times 3^{\frac{2}{3}}-3\sqrt{5}-18\sqrt{2}\approx -21.76362894$$

Solution Steps

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$\sqrt[3]{243}-2\times 5\sqrt{5}-3\sqrt{72}+3\sqrt{45}+2\sqrt[3]{9}-\sqrt{20}$$

Multiply -2 and 5 to get -10.

$$\sqrt[3]{243}-10\sqrt{5}-3\sqrt{72}+3\sqrt{45}+2\sqrt[3]{9}-\sqrt{20}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\sqrt[3]{243}-10\sqrt{5}-3\times 6\sqrt{2}+3\sqrt{45}+2\sqrt[3]{9}-\sqrt{20}$$

Multiply -3 and 6 to get -18.

$$\sqrt[3]{243}-10\sqrt{5}-18\sqrt{2}+3\sqrt{45}+2\sqrt[3]{9}-\sqrt{20}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\sqrt[3]{243}-10\sqrt{5}-18\sqrt{2}+3\times 3\sqrt{5}+2\sqrt[3]{9}-\sqrt{20}$$

Multiply 3 and 3 to get 9.

$$\sqrt[3]{243}-10\sqrt{5}-18\sqrt{2}+9\sqrt{5}+2\sqrt[3]{9}-\sqrt{20}$$

Combine -10\sqrt{5} and 9\sqrt{5} to get -\sqrt{5}.

$$\sqrt[3]{243}-\sqrt{5}-18\sqrt{2}+2\sqrt[3]{9}-\sqrt{20}$$

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}.

$$\sqrt[3]{243}-\sqrt{5}-18\sqrt{2}+2\sqrt[3]{9}-2\sqrt{5}$$

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

$$\sqrt[3]{243}-3\sqrt{5}-18\sqrt{2}+2\sqrt[3]{9}$$