Solve 17.4sqrt{5}-2sqrt{2}-sqrt{20}-sqrt{18}=

$$17.4 \sqrt { 5 } - 2 \sqrt { 2 } - \sqrt { 20 } - \sqrt { 18 } =$$

Evaluate

$$\frac{77\sqrt{5}}{5}-5\sqrt{2}\approx 27.364379042$$

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}.

$$17.4\sqrt{5}-2\sqrt{2}-2\sqrt{5}-\sqrt{18}$$

Combine 17.4\sqrt{5} and -2\sqrt{5} to get 15.4\sqrt{5}.

$$15.4\sqrt{5}-2\sqrt{2}-\sqrt{18}$$

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}.

$$15.4\sqrt{5}-2\sqrt{2}-3\sqrt{2}$$

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

$$15.4\sqrt{5}-5\sqrt{2}$$