Solve sqrt{72}+sqrt{50}288-sqrt{200}

$$\sqrt{ 72 } + \sqrt{ 50 } 288- \sqrt{ 200 }$$

Evaluate

$$1436\sqrt{2}\approx 2030.810675568$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$6\sqrt{2}+288\sqrt{50}-\sqrt{200}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$6\sqrt{2}+288\times 5\sqrt{2}-\sqrt{200}$$

Multiply 288 and 5 to get 1440.

$$6\sqrt{2}+1440\sqrt{2}-\sqrt{200}$$

Combine 6\sqrt{2} and 1440\sqrt{2} to get 1446\sqrt{2}.

$$1446\sqrt{2}-\sqrt{200}$$

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}.

$$1446\sqrt{2}-10\sqrt{2}$$

Combine 1446\sqrt{2} and -10\sqrt{2} to get 1436\sqrt{2}.

$$1436\sqrt{2}$$