Solve 3sqrt{45}-sqrt{125}+sqrt{20}

$$3 \sqrt{ 45 } - \sqrt{ 125 } + \sqrt{ 20 }$$

Evaluate

$$6\sqrt{5}\approx 13.416407865$$

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}.

$$3\times 3\sqrt{5}-\sqrt{125}+\sqrt{20}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{5}-\sqrt{125}+\sqrt{20}$$

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}.

$$9\sqrt{5}-5\sqrt{5}+\sqrt{20}$$

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

$$4\sqrt{5}+\sqrt{20}$$

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}.

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

Combine 4\sqrt{5} and 2\sqrt{5} to get 6\sqrt{5}.

$$6\sqrt{5}$$