Solve frac{6sqrt{6}}{sqrt{18}}

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

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

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}.

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

Cancel out 3 in both numerator and denominator.

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

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

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

The square of \sqrt{2} is 2.

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

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}.

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

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

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

Cancel out 2 and 2.

$$2\sqrt{3}$$