Solve 3sqrt{22/3}

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

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

Multiply 2 and 3 to get 6.

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

Add 6 and 2 to get 8.

$$3\sqrt{\frac{8}{3}}$$

Rewrite the square root of the division \sqrt{\frac{8}{3}} as the division of square roots \frac{\sqrt{8}}{\sqrt{3}}.

$$3\times \frac{\sqrt{8}}{\sqrt{3}}$$

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}.

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

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

Cancel out 3 and 3.

$$2\sqrt{6}$$