Solve 3sqrt{8}-2sqrt{1/3}

$$3 \sqrt { 8 } - 2 \sqrt { \frac { 1 } { 3 } }$$

Evaluate

$$-\frac{2\sqrt{3}}{3}+6\sqrt{2}\approx 7.330580836$$

Short Solution Steps

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}.

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

Multiply 3 and 2 to get 6.

$$6\sqrt{2}-2\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$6\sqrt{2}-2\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$6\sqrt{2}-2\times \frac{1}{\sqrt{3}}$$

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

$$6\sqrt{2}-2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$6\sqrt{2}-2\times \frac{\sqrt{3}}{3}$$

Express -2\times \frac{\sqrt{3}}{3} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 6\sqrt{2} times \frac{3}{3}.

$$\frac{3\times 6\sqrt{2}}{3}+\frac{-2\sqrt{3}}{3}$$

Since \frac{3\times 6\sqrt{2}}{3} and \frac{-2\sqrt{3}}{3} have the same denominator, add them by adding their numerators.

$$\frac{3\times 6\sqrt{2}-2\sqrt{3}}{3}$$

Do the multiplications in 3\times 6\sqrt{2}-2\sqrt{3}.

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