Solve 2/sqrt{3}+sqrt{2}7+(sqrt{3}-1)^0-(sqrt{3}-sqrt{2})

$$\frac { 2 } { \sqrt { 3 } } + \sqrt { 2 } 7 + ( \sqrt { 3 } - 1 ) ^ { 0 } - ( \sqrt { 3 } - \sqrt { 2 } )$$

Evaluate

$$-\frac{\sqrt{3}}{3}+8\sqrt{2}+1\approx 11.73635823$$

Short Solution Steps

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

$$\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+7\sqrt{2}+\left(\sqrt{3}-1\right)^{0}-\left(\sqrt{3}-\sqrt{2}\right)$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{3}}{3}+7\sqrt{2}+\left(\sqrt{3}-1\right)^{0}-\left(\sqrt{3}-\sqrt{2}\right)$$

Calculate \sqrt{3}-1 to the power of 0 and get 1.

$$\frac{2\sqrt{3}}{3}+7\sqrt{2}+1-\left(\sqrt{3}-\sqrt{2}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7\sqrt{2}+1 times \frac{3}{3}.

$$\frac{2\sqrt{3}}{3}+\frac{3\left(7\sqrt{2}+1\right)}{3}-\left(\sqrt{3}-\sqrt{2}\right)$$

Since \frac{2\sqrt{3}}{3} and \frac{3\left(7\sqrt{2}+1\right)}{3} have the same denominator, add them by adding their numerators.

$$\frac{2\sqrt{3}+3\left(7\sqrt{2}+1\right)}{3}-\left(\sqrt{3}-\sqrt{2}\right)$$

Do the multiplications in 2\sqrt{3}+3\left(7\sqrt{2}+1\right).

$$\frac{2\sqrt{3}+21\sqrt{2}+3}{3}-\left(\sqrt{3}-\sqrt{2}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{3}-\sqrt{2} times \frac{3}{3}.

$$\frac{2\sqrt{3}+21\sqrt{2}+3}{3}-\frac{3\left(\sqrt{3}-\sqrt{2}\right)}{3}$$

Since \frac{2\sqrt{3}+21\sqrt{2}+3}{3} and \frac{3\left(\sqrt{3}-\sqrt{2}\right)}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\sqrt{3}+21\sqrt{2}+3-3\left(\sqrt{3}-\sqrt{2}\right)}{3}$$

Do the multiplications in 2\sqrt{3}+21\sqrt{2}+3-3\left(\sqrt{3}-\sqrt{2}\right).

$$\frac{2\sqrt{3}+21\sqrt{2}+3-3\sqrt{3}+3\sqrt{2}}{3}$$

Do the calculations in 2\sqrt{3}+21\sqrt{2}+3-3\sqrt{3}+3\sqrt{2}.

$$\frac{-\sqrt{3}+24\sqrt{2}+3}{3}$$