Solve 4sqrt{20}-3sqrt{45}

$$4 \sqrt { 20 } - 3 \sqrt { 45 }$$

Evaluate

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

Solution Steps

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}.

$$4\times 2\sqrt{5}-3\sqrt{45}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{5}-3\sqrt{45}$$

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}.

$$8\sqrt{5}-3\times 3\sqrt{5}$$

Multiply -3 and 3 to get -9.

$$8\sqrt{5}-9\sqrt{5}$$

Combine 8\sqrt{5} and -9\sqrt{5} to get -\sqrt{5}.

$$-\sqrt{5}$$