Solve 3sqrt{20}+5sqrt{45}-2sqrt{80}

$$3 \sqrt { 20 } + 5 \sqrt { 45 } - 2 \sqrt { 80 }$$

Evaluate

$$13\sqrt{5}\approx 29.068883707$$

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}.

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

Multiply 3 and 2 to get 6.

$$6\sqrt{5}+5\sqrt{45}-2\sqrt{80}$$

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}.

$$6\sqrt{5}+5\times 3\sqrt{5}-2\sqrt{80}$$

Multiply 5 and 3 to get 15.

$$6\sqrt{5}+15\sqrt{5}-2\sqrt{80}$$

Combine 6\sqrt{5} and 15\sqrt{5} to get 21\sqrt{5}.

$$21\sqrt{5}-2\sqrt{80}$$

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}.

$$21\sqrt{5}-2\times 4\sqrt{5}$$

Multiply -2 and 4 to get -8.

$$21\sqrt{5}-8\sqrt{5}$$

Combine 21\sqrt{5} and -8\sqrt{5} to get 13\sqrt{5}.

$$13\sqrt{5}$$