Solve 2sqrt{20}-4sqrt{45}+sqrt{12}

$$2 \sqrt { 20 } - 4 \sqrt { 45 } + \sqrt { 12 }$$

Evaluate

$$2\left(\sqrt{3}-4\sqrt{5}\right)\approx -14.424442205$$

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}.

$$2\times 2\sqrt{5}-4\sqrt{45}+\sqrt{12}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{5}-4\sqrt{45}+\sqrt{12}$$

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}.

$$4\sqrt{5}-4\times 3\sqrt{5}+\sqrt{12}$$

Multiply -4 and 3 to get -12.

$$4\sqrt{5}-12\sqrt{5}+\sqrt{12}$$

Combine 4\sqrt{5} and -12\sqrt{5} to get -8\sqrt{5}.

$$-8\sqrt{5}+\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$-8\sqrt{5}+2\sqrt{3}$$