Solve 3sqrt{125}-2sqrt{45}+sqrt{80}

$$3 \sqrt{ 125 } -2 \sqrt{ 45 } + \sqrt{ 80 }$$

Evaluate

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

Solution Steps

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

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

Multiply 3 and 5 to get 15.

$$15\sqrt{5}-2\sqrt{45}+\sqrt{80}$$

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}.

$$15\sqrt{5}-2\times 3\sqrt{5}+\sqrt{80}$$

Multiply -2 and 3 to get -6.

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

Combine 15\sqrt{5} and -6\sqrt{5} to get 9\sqrt{5}.

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

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}.

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

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

$$13\sqrt{5}$$