Solve sqrt{20}-sqrt{45}-sqrt{80}

$$\sqrt { 20 } - \sqrt { 45 } - \sqrt { 80 }$$

Evaluate

$$-5\sqrt{5}\approx -11.180339887$$

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}.

$$2\sqrt{5}-\sqrt{45}-\sqrt{80}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$2\sqrt{5}-3\sqrt{5}-\sqrt{80}$$

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

$$-\sqrt{5}-\sqrt{80}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$-\sqrt{5}-4\sqrt{5}$$

Combine -\sqrt{5} and -4\sqrt{5} to get -5\sqrt{5}.

$$-5\sqrt{5}$$