Solve 2sqrt{6}div2/3sqrt{3}

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

Evaluate

$$9\sqrt{2}\approx 12.727922061$$

Solution Steps

Divide 2\sqrt{6} by \frac{2}{3} by multiplying 2\sqrt{6} by the reciprocal of \frac{2}{3}.

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

Cancel out 2 and 2.

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 3 and 3 to get 9.

$$9\sqrt{2}$$