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

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

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}.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{5}+3\sqrt{45}$$

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}.

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

Multiply 3 and 3 to get 9.

$$4\sqrt{5}+9\sqrt{5}$$

Combine 4\sqrt{5} and 9\sqrt{5} to get 13\sqrt{5}.

$$13\sqrt{5}$$