Solve sqrt{18}-sqrt{12}-sqrt{2}+1/sqrt{3}

$$\sqrt { 18 } - \sqrt { 12 } - \sqrt { 2 } + \frac { 1 } { \sqrt { 3 } }$$

Evaluate

$$-\frac{5\sqrt{3}}{3}+2\sqrt{2}\approx -0.058324221$$

Solution Steps

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}.

$$3\sqrt{2}-\sqrt{12}-\sqrt{2}+\frac{1}{\sqrt{3}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$3\sqrt{2}-2\sqrt{3}-\sqrt{2}+\frac{1}{\sqrt{3}}$$

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

$$2\sqrt{2}-2\sqrt{3}+\frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2\sqrt{2}-2\sqrt{3}+\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Combine -2\sqrt{3} and \frac{\sqrt{3}}{3} to get -\frac{5}{3}\sqrt{3}.

$$2\sqrt{2}-\frac{5}{3}\sqrt{3}$$