Solve 2sqrt{20}-sqrt{20}+3sqrt{20}-2sqrt{45}

$$2 \sqrt { 20 } - \sqrt { 20 } + 3 \sqrt { 20 } - 2 \sqrt { 45 }$$

Evaluate

$$2\sqrt{5}\approx 4.472135955$$

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}.

$$2\times 2\sqrt{5}-\sqrt{20}+3\sqrt{20}-2\sqrt{45}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{5}-\sqrt{20}+3\sqrt{20}-2\sqrt{45}$$

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}.

$$4\sqrt{5}-2\sqrt{5}+3\sqrt{20}-2\sqrt{45}$$

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

$$2\sqrt{5}+3\sqrt{20}-2\sqrt{45}$$

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}.

$$2\sqrt{5}+3\times 2\sqrt{5}-2\sqrt{45}$$

Multiply 3 and 2 to get 6.

$$2\sqrt{5}+6\sqrt{5}-2\sqrt{45}$$

Combine 2\sqrt{5} and 6\sqrt{5} to get 8\sqrt{5}.

$$8\sqrt{5}-2\sqrt{45}$$

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}.

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

Multiply -2 and 3 to get -6.

$$8\sqrt{5}-6\sqrt{5}$$

Combine 8\sqrt{5} and -6\sqrt{5} to get 2\sqrt{5}.

$$2\sqrt{5}$$