Solve sqrt{5}+2sqrt{45}-3sqrt{125}=

$$\sqrt { 5 } + 2 \sqrt { 45 } - 3 \sqrt { 125 } =$$

Evaluate

$$-8\sqrt{5}\approx -17.88854382$$

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}.

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

Multiply 2 and 3 to get 6.

$$\sqrt{5}+6\sqrt{5}-3\sqrt{125}$$

Combine \sqrt{5} and 6\sqrt{5} to get 7\sqrt{5}.

$$7\sqrt{5}-3\sqrt{125}$$

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}.

$$7\sqrt{5}-3\times 5\sqrt{5}$$

Multiply -3 and 5 to get -15.

$$7\sqrt{5}-15\sqrt{5}$$

Combine 7\sqrt{5} and -15\sqrt{5} to get -8\sqrt{5}.

$$-8\sqrt{5}$$