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

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

Evaluate

$$\sqrt{5}\approx 2.236067977$$

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}.

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

Multiply 2 and 5 to get 10.

$$10\sqrt{5}-3\sqrt{45}$$

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}.

$$10\sqrt{5}-3\times 3\sqrt{5}$$

Multiply -3 and 3 to get -9.

$$10\sqrt{5}-9\sqrt{5}$$

Combine 10\sqrt{5} and -9\sqrt{5} to get \sqrt{5}.

$$\sqrt{5}$$