Solve 1/3sqrt{27}-sqrt{8}-sqrt{3}+2/3+sqrt{18}+sqrt{2}

$$\frac { 1 } { 3 } \sqrt { 27 } - \sqrt { 8 } - \sqrt { 3 } + \frac { 2 } { 3 } + \sqrt { 18 } + \sqrt { 2 }$$

Evaluate

$$2\sqrt{2}+\frac{2}{3}\approx 3.495093791$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{1}{3}\times 3\sqrt{3}-\sqrt{8}-\sqrt{3}+\frac{2}{3}+\sqrt{18}+\sqrt{2}$$

Cancel out 3 and 3.

$$\sqrt{3}-\sqrt{8}-\sqrt{3}+\frac{2}{3}+\sqrt{18}+\sqrt{2}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Combine \sqrt{3} and -\sqrt{3} to get 0.

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

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}.

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

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

$$\sqrt{2}+\frac{2}{3}+\sqrt{2}$$

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

$$2\sqrt{2}+\frac{2}{3}$$

Factor

$$\frac{2 {(3 \sqrt{2} + 1)}}{3} = 3.4950937914128573$$