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

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

Evaluate

$$14\sqrt{5}\approx 31.304951685$$

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}.

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

Combine 5\sqrt{5} and -3\sqrt{5} to get 2\sqrt{5}.

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

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}.

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

Multiply 3 and 4 to get 12.

$$2\sqrt{5}+12\sqrt{5}$$

Combine 2\sqrt{5} and 12\sqrt{5} to get 14\sqrt{5}.

$$14\sqrt{5}$$