Solve frac{12sqrt{18}}{3sqrt{6}}

$$\frac { 12 \sqrt { 18 } } { 3 \sqrt { 6 } }$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{4\sqrt{18}}{\sqrt{6}}$$

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}.

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

Multiply 4 and 3 to get 12.

$$\frac{12\sqrt{2}}{\sqrt{6}}$$

Rationalize the denominator of \frac{12\sqrt{2}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{12\sqrt{2}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{12\sqrt{2}\sqrt{6}}{6}$$

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

$$\frac{12\sqrt{2}\sqrt{2}\sqrt{3}}{6}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{12\times 2\sqrt{3}}{6}$$

Multiply 12 and 2 to get 24.

$$\frac{24\sqrt{3}}{6}$$

Divide 24\sqrt{3} by 6 to get 4\sqrt{3}.

$$4\sqrt{3}$$