Solve -sqrt{45}-3sqrt{45}+3sqrt{20}

$$- \sqrt { 45 } - 3 \sqrt { 45 } + 3 \sqrt { 20 }$$

Evaluate

$$-6\sqrt{5}\approx -13.416407865$$

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}.

$$-3\sqrt{5}-3\sqrt{45}+3\sqrt{20}$$

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}.

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

Multiply -3 and 3 to get -9.

$$-3\sqrt{5}-9\sqrt{5}+3\sqrt{20}$$

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}.

$$-3\sqrt{5}-9\sqrt{5}+3\times 2\sqrt{5}$$

Multiply 3 and 2 to get 6.

$$-3\sqrt{5}-9\sqrt{5}+6\sqrt{5}$$

Combine -9\sqrt{5} and 6\sqrt{5} to get -3\sqrt{5}.

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

Combine -3\sqrt{5} and -3\sqrt{5} to get -6\sqrt{5}.

$$-6\sqrt{5}$$