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

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

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

Solution Steps

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

$$6\sqrt{2}+\sqrt{18}-2\sqrt{18}$$

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}.

$$6\sqrt{2}+3\sqrt{2}-2\sqrt{18}$$

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

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

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}.

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

Multiply -2 and 3 to get -6.

$$9\sqrt{2}-6\sqrt{2}$$

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

$$3\sqrt{2}$$