Solve sqrt{200}-sqrt{32}

$$\sqrt{ 200 } - \sqrt{ 32 }$$

Evaluate

$$6\sqrt{2}\approx 8.485281374$$

Solution Steps

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}.

$$10\sqrt{2}-\sqrt{32}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

Combine 10\sqrt{2} and -4\sqrt{2} to get 6\sqrt{2}.

$$6\sqrt{2}$$