Solve 4sqrt{2}+sqrt{50}-sqrt{18}

$$4 \sqrt { 2 } + \sqrt { 50 } - \sqrt { 18 }$$

Evaluate

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

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}.

$$4\sqrt{2}+5\sqrt{2}-\sqrt{18}$$

Combine 4\sqrt{2} and 5\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}-\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$9\sqrt{2}-3\sqrt{2}$$

Combine 9\sqrt{2} and -3\sqrt{2} to get 6\sqrt{2}.

$$6\sqrt{2}$$