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

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

Evaluate

$$\sqrt{5}\approx 2.236067977$$

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}.

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

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}.

$$2\sqrt{5}-4\sqrt{5}+\sqrt{45}$$

Combine 2\sqrt{5} and -4\sqrt{5} to get -2\sqrt{5}.

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

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}.

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

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

$$\sqrt{5}$$