Solve 12(frac{sqrt{2}}{2})^2*1/2+6(1/sqrt{3})-1

$$12 ( \frac { \sqrt { 2 } } { 2 } ) ^ { 2 } \cdot \frac { 1 } { 2 } + 6 ( \frac { 1 } { \sqrt { 3 } } ) - 1$$

Evaluate

$$2\left(\sqrt{3}+1\right)\approx 5.464101615$$

Solution Steps

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

$$12\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}\times \frac{1}{2}+6\times \frac{1}{\sqrt{3}}-1$$

Multiply 12 and \frac{1}{2} to get 6.

$$6\times \frac{\left(\sqrt{2}\right)^{2}}{2^{2}}+6\times \frac{1}{\sqrt{3}}-1$$

The square of \sqrt{2} is 2.

$$6\times \frac{2}{2^{2}}+6\times \frac{1}{\sqrt{3}}-1$$

Calculate 2 to the power of 2 and get 4.

$$6\times \frac{2}{4}+6\times \frac{1}{\sqrt{3}}-1$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$6\times \frac{1}{2}+6\times \frac{1}{\sqrt{3}}-1$$

Multiply 6 and \frac{1}{2} to get 3.

$$3+6\times \frac{1}{\sqrt{3}}-1$$

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

$$3+6\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-1$$

The square of \sqrt{3} is 3.

$$3+6\times \frac{\sqrt{3}}{3}-1$$

Cancel out 3, the greatest common factor in 6 and 3.

$$3+2\sqrt{3}-1$$

Subtract 1 from 3 to get 2.

$$2+2\sqrt{3}$$

Factor

$$2 {(\sqrt{3} + 1)} = 5.464101615$$