Solve frac{4sqrt{12}}{9sqrt{6}}

$$\frac { 4 \sqrt { 12 } } { 9 \sqrt { 6 } }$$

Evaluate

$$\frac{4\sqrt{2}}{9}\approx 0.628539361$$

Solution Steps

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}.

$$\frac{4\times 2\sqrt{3}}{9\sqrt{6}}$$

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{3}}{9\sqrt{6}}$$

Rationalize the denominator of \frac{8\sqrt{3}}{9\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{8\sqrt{3}\sqrt{6}}{9\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{8\sqrt{3}\sqrt{6}}{9\times 6}$$

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}.

$$\frac{8\sqrt{3}\sqrt{3}\sqrt{2}}{9\times 6}$$

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

$$\frac{8\times 3\sqrt{2}}{9\times 6}$$

Multiply 9 and 6 to get 54.

$$\frac{8\times 3\sqrt{2}}{54}$$

Multiply 8 and 3 to get 24.

$$\frac{24\sqrt{2}}{54}$$

Divide 24\sqrt{2} by 54 to get \frac{4}{9}\sqrt{2}.

$$\frac{4}{9}\sqrt{2}$$