Solve 3sqrt{45}-2sqrt{80}+4sqrt{20}

$$3 \sqrt { 45 } - 2 \sqrt { 80 } + 4 \sqrt { 20 }$$

Evaluate

$$9\sqrt{5}\approx 20.124611797$$

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}.

$$3\times 3\sqrt{5}-2\sqrt{80}+4\sqrt{20}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{5}-2\sqrt{80}+4\sqrt{20}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$9\sqrt{5}-2\times 4\sqrt{5}+4\sqrt{20}$$

Multiply -2 and 4 to get -8.

$$9\sqrt{5}-8\sqrt{5}+4\sqrt{20}$$

Combine 9\sqrt{5} and -8\sqrt{5} to get \sqrt{5}.

$$\sqrt{5}+4\sqrt{20}$$

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}.

$$\sqrt{5}+4\times 2\sqrt{5}$$

Multiply 4 and 2 to get 8.

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

Combine \sqrt{5} and 8\sqrt{5} to get 9\sqrt{5}.

$$9\sqrt{5}$$