Solve 6sqrt{6}divsqrt{72}div2

$$6 \sqrt { 6 } \div \sqrt { 72 } \div 2$$

Evaluate

$$\frac{\sqrt{3}}{2}\approx 0.866025404$$

Solution Steps

Express \frac{\frac{6\sqrt{6}}{\sqrt{72}}}{2} as a single fraction.

$$\frac{6\sqrt{6}}{\sqrt{72}\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{6}}{\sqrt{72}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

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

Cancel out 3 in both numerator and denominator.

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

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

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

The square of \sqrt{2} is 2.

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

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}.

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

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

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

Multiply 2 and 2 to get 4.

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

Divide 2\sqrt{3} by 4 to get \frac{1}{2}\sqrt{3}.

$$\frac{1}{2}\sqrt{3}$$