Solve 5sqrt{18}+sqrt{50}-sqrt{125}+3sqrt{5}

$$5 \sqrt { 18 } + \sqrt { 50 } - \sqrt { 125 } + 3 \sqrt { 5 }$$

Evaluate

$$20\sqrt{2}-2\sqrt{5}\approx 23.812135292$$

Solution Steps

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}.

$$5\times 3\sqrt{2}+\sqrt{50}-\sqrt{125}+3\sqrt{5}$$

Multiply 5 and 3 to get 15.

$$15\sqrt{2}+\sqrt{50}-\sqrt{125}+3\sqrt{5}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

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

Combine 15\sqrt{2} and 5\sqrt{2} to get 20\sqrt{2}.

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

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}.

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

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

$$20\sqrt{2}-2\sqrt{5}$$