Solve sqrt{125}-sqrt{180}+sqrt{320}

$$\sqrt { 125 } - \sqrt { 180 } + \sqrt { 320 }$$

Evaluate

$$7\sqrt{5}\approx 15.652475842$$

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}.

$$5\sqrt{5}-\sqrt{180}+\sqrt{320}$$

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}.

$$5\sqrt{5}-6\sqrt{5}+\sqrt{320}$$

Combine 5\sqrt{5} and -6\sqrt{5} to get -\sqrt{5}.

$$-\sqrt{5}+\sqrt{320}$$

Factor 320=8^{2}\times 5. Rewrite the square root of the product \sqrt{8^{2}\times 5} as the product of square roots \sqrt{8^{2}}\sqrt{5}. Take the square root of 8^{2}.

$$-\sqrt{5}+8\sqrt{5}$$

Combine -\sqrt{5} and 8\sqrt{5} to get 7\sqrt{5}.

$$7\sqrt{5}$$