Solve 3sqrt{125}+2sqrt{20}-5sqrt{45}

$$3 \sqrt { 125 } + 2 \sqrt { 20 } - 5 \sqrt { 45 }$$

Evaluate

$$4\sqrt{5}\approx 8.94427191$$

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}.

$$3\times 5\sqrt{5}+2\sqrt{20}-5\sqrt{45}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{5}+2\sqrt{20}-5\sqrt{45}$$

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}.

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

Multiply 2 and 2 to get 4.

$$15\sqrt{5}+4\sqrt{5}-5\sqrt{45}$$

Combine 15\sqrt{5} and 4\sqrt{5} to get 19\sqrt{5}.

$$19\sqrt{5}-5\sqrt{45}$$

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}.

$$19\sqrt{5}-5\times 3\sqrt{5}$$

Multiply -5 and 3 to get -15.

$$19\sqrt{5}-15\sqrt{5}$$

Combine 19\sqrt{5} and -15\sqrt{5} to get 4\sqrt{5}.

$$4\sqrt{5}$$