Solve sqrt{50}+sqrt{200}-sqrt{450}

$$\sqrt{ 50 } + \sqrt{ 200 } - \sqrt{ 450 }$$

Evaluate

$$0$$

Solution Steps

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}.

$$5\sqrt{2}+\sqrt{200}-\sqrt{450}$$

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}.

$$5\sqrt{2}+10\sqrt{2}-\sqrt{450}$$

Combine 5\sqrt{2} and 10\sqrt{2} to get 15\sqrt{2}.

$$15\sqrt{2}-\sqrt{450}$$

Factor 450=15^{2}\times 2. Rewrite the square root of the product \sqrt{15^{2}\times 2} as the product of square roots \sqrt{15^{2}}\sqrt{2}. Take the square root of 15^{2}.

$$15\sqrt{2}-15\sqrt{2}$$

Combine 15\sqrt{2} and -15\sqrt{2} to get 0.

$$0$$

Factor

$$0$$