Solve sqrt{45}-sqrt{125}-sqrt{20}

$$\sqrt { 45 } - \sqrt { 125 } - \sqrt { 20 }$$

Evaluate

$$-4\sqrt{5}\approx -8.94427191$$

Solution Steps

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}.

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

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}.

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

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

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

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}.

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

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

$$-4\sqrt{5}$$