Solve sqrt{45}+2sqrt{80}

$$\sqrt { 45 } + 2 \sqrt { 80 }$$

Evaluate

$$11\sqrt{5}\approx 24.596747752$$

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}.

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

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}.

$$3\sqrt{5}+2\times 4\sqrt{5}$$

Multiply 2 and 4 to get 8.

$$3\sqrt{5}+8\sqrt{5}$$

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

$$11\sqrt{5}$$