Solve 10sqrt{5}-sqrt{20}+4sqrt{125}-3sqrt{180}

$$10 \sqrt { 5 } - \sqrt { 20 } + 4 \sqrt { 125 } - 3 \sqrt { 180 }$$

Evaluate

$$10\sqrt{5}\approx 22.360679775$$

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}.

$$10\sqrt{5}-2\sqrt{5}+4\sqrt{125}-3\sqrt{180}$$

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

$$8\sqrt{5}+4\sqrt{125}-3\sqrt{180}$$

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}.

$$8\sqrt{5}+4\times 5\sqrt{5}-3\sqrt{180}$$

Multiply 4 and 5 to get 20.

$$8\sqrt{5}+20\sqrt{5}-3\sqrt{180}$$

Combine 8\sqrt{5} and 20\sqrt{5} to get 28\sqrt{5}.

$$28\sqrt{5}-3\sqrt{180}$$

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}.

$$28\sqrt{5}-3\times 6\sqrt{5}$$

Multiply -3 and 6 to get -18.

$$28\sqrt{5}-18\sqrt{5}$$

Combine 28\sqrt{5} and -18\sqrt{5} to get 10\sqrt{5}.

$$10\sqrt{5}$$