Solve 3sqrt{50}-2sqrt{18}-sqrt{2}

$$3 \sqrt{ 50 } -2 \sqrt{ 18 } - \sqrt{ 2 }$$

Evaluate

$$8\sqrt{2}\approx 11.313708499$$

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}.

$$3\times 5\sqrt{2}-2\sqrt{18}-\sqrt{2}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{2}-2\sqrt{18}-\sqrt{2}$$

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}.

$$15\sqrt{2}-2\times 3\sqrt{2}-\sqrt{2}$$

Multiply -2 and 3 to get -6.

$$15\sqrt{2}-6\sqrt{2}-\sqrt{2}$$

Combine 15\sqrt{2} and -6\sqrt{2} to get 9\sqrt{2}.

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

Combine 9\sqrt{2} and -\sqrt{2} to get 8\sqrt{2}.

$$8\sqrt{2}$$