Solve frac{2sqrt{6}}{4sqrt{2}}*frac{sqrt{2}}{sqrt{2}}

$$\frac { 2 \sqrt { 6 } } { 4 \sqrt { 2 } } \cdot \frac { \sqrt { 2 } } { \sqrt { 2 } }$$

Evaluate

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

Solution Steps

Divide \sqrt{2} by \sqrt{2} to get 1.

$$\frac{2\sqrt{6}}{4\sqrt{2}}\times 1$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{6}}{2\sqrt{2}}\times 1$$

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

$$\frac{\sqrt{6}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}\times 1$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{6}\sqrt{2}}{2\times 2}\times 1$$

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}.

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

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

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

Multiply 2 and 2 to get 4.

$$\frac{2\sqrt{3}}{4}\times 1$$

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

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

Multiply \frac{1}{2} and 1 to get \frac{1}{2}.

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