Solve 3sqrt{2}-sqrt{20}+5sqrt{18}-sqrt{125}

$$3 \sqrt { 2 } - \sqrt { 20 } + 5 \sqrt { 18 } - \sqrt { 125 }$$

Evaluate

$$18\sqrt{2}-7\sqrt{5}\approx 9.80336828$$

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}.

$$3\sqrt{2}-2\sqrt{5}+5\sqrt{18}-\sqrt{125}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$3\sqrt{2}-2\sqrt{5}+5\times 3\sqrt{2}-\sqrt{125}$$

Multiply 5 and 3 to get 15.

$$3\sqrt{2}-2\sqrt{5}+15\sqrt{2}-\sqrt{125}$$

Combine 3\sqrt{2} and 15\sqrt{2} to get 18\sqrt{2}.

$$18\sqrt{2}-2\sqrt{5}-\sqrt{125}$$

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}.

$$18\sqrt{2}-2\sqrt{5}-5\sqrt{5}$$

Combine -2\sqrt{5} and -5\sqrt{5} to get -7\sqrt{5}.

$$18\sqrt{2}-7\sqrt{5}$$