Solve 3sqrt{800}-4sqrt{200}

$$3 \sqrt { 800 } - 4 \sqrt { 200 }$$

Evaluate

$$20\sqrt{2}\approx 28.284271247$$

Solution Steps

Factor 800=20^{2}\times 2. Rewrite the square root of the product \sqrt{20^{2}\times 2} as the product of square roots \sqrt{20^{2}}\sqrt{2}. Take the square root of 20^{2}.

$$3\times 20\sqrt{2}-4\sqrt{200}$$

Multiply 3 and 20 to get 60.

$$60\sqrt{2}-4\sqrt{200}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$60\sqrt{2}-4\times 10\sqrt{2}$$

Multiply -4 and 10 to get -40.

$$60\sqrt{2}-40\sqrt{2}$$

Combine 60\sqrt{2} and -40\sqrt{2} to get 20\sqrt{2}.

$$20\sqrt{2}$$