Solve 4/4sqrt{2}*frac{sqrt{3}}{sqrt{2}}=

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

Evaluate

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

Solution Steps

Rationalize the denominator of \frac{4}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}\times \frac{\sqrt{3}}{\sqrt{2}}$$

The square of \sqrt{2} is 2.

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

Cancel out 4 in both numerator and denominator.

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

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{2}\times \frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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

Multiply \frac{\sqrt{2}}{2} times \frac{\sqrt{6}}{2} by multiplying numerator times numerator and denominator times denominator.

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

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}.

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

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}.

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