Solve (1/sqrt{3}*frac{sqrt{2}}{2})+(frac{sqrt{3}}{2}*frac{sqrt{3}}{2})

$$( \frac { 1 } { \sqrt { 3 } } \times \frac { \sqrt { 2 } } { 2 } ) + ( \frac { \sqrt { 3 } } { 2 } \times \frac { \sqrt { 3 } } { 2 } )$$

Evaluate

$$\frac{\sqrt{6}}{6}+\frac{3}{4}\approx 1.15824829$$

Short Solution Steps

Multiply \frac{\sqrt{3}}{2} and \frac{\sqrt{3}}{2} to get \left(\frac{\sqrt{3}}{2}\right)^{2}.

$$\frac{1}{\sqrt{3}}\times \frac{\sqrt{2}}{2}+\left(\frac{\sqrt{3}}{2}\right)^{2}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply \frac{\sqrt{3}}{3} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

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

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\times 2 and 2^{2} is 12. Multiply \frac{\sqrt{3}\sqrt{2}}{3\times 2} times \frac{2}{2}. Multiply \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} times \frac{3}{3}.

$$\frac{2\sqrt{3}\sqrt{2}}{12}+\frac{3\left(\sqrt{3}\right)^{2}}{12}$$

Since \frac{2\sqrt{3}\sqrt{2}}{12} and \frac{3\left(\sqrt{3}\right)^{2}}{12} have the same denominator, add them by adding their numerators.

$$\frac{2\sqrt{3}\sqrt{2}+3\left(\sqrt{3}\right)^{2}}{12}$$

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

$$\frac{\sqrt{6}}{3\times 2}+\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}$$

Multiply 3 and 2 to get 6.

$$\frac{\sqrt{6}}{6}+\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}$$

The square of \sqrt{3} is 3.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{\sqrt{6}}{6}+\frac{3}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 4 is 12. Multiply \frac{\sqrt{6}}{6} times \frac{2}{2}. Multiply \frac{3}{4} times \frac{3}{3}.

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

Since \frac{2\sqrt{6}}{12} and \frac{3\times 3}{12} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\sqrt{6}+3\times 3.

$$\frac{2\sqrt{6}+9}{12}$$

Factor

$$\frac{2 \sqrt{6} + 9}{12} = 1.158248290463863$$