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

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

Evaluate

$$3\sqrt{5}\approx 6.708203932$$

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}.

$$2\sqrt{5}+3\sqrt{45}-2\sqrt{80}$$

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}.

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

Multiply 3 and 3 to get 9.

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

Combine 2\sqrt{5} and 9\sqrt{5} to get 11\sqrt{5}.

$$11\sqrt{5}-2\sqrt{80}$$

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}.

$$11\sqrt{5}-2\times 4\sqrt{5}$$

Multiply -2 and 4 to get -8.

$$11\sqrt{5}-8\sqrt{5}$$

Combine 11\sqrt{5} and -8\sqrt{5} to get 3\sqrt{5}.

$$3\sqrt{5}$$