Solve 3/sqrt{3}-(sqrt{3})^2+(pi+3)^0-sqrt{2}+(sqrt{3}-21)

$$\frac { 3 } { \sqrt { 3 } } - ( \sqrt { 3 } ) ^ { 2 } + ( \pi + 3 ) ^ { 0 } - \sqrt { 2 } + ( \sqrt { 3 } - 21 )$$

Evaluate

$$2\sqrt{3}-\sqrt{2}-23\approx -20.950111947$$

Solution Steps

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

$$\frac{3\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\left(\sqrt{3}\right)^{2}+\left(\pi +3\right)^{0}-\sqrt{2}+\sqrt{3}-21$$

The square of \sqrt{3} is 3.

$$\frac{3\sqrt{3}}{3}-\left(\sqrt{3}\right)^{2}+\left(\pi +3\right)^{0}-\sqrt{2}+\sqrt{3}-21$$

Cancel out 3 and 3.

$$\sqrt{3}-\left(\sqrt{3}\right)^{2}+\left(\pi +3\right)^{0}-\sqrt{2}+\sqrt{3}-21$$

The square of \sqrt{3} is 3.

$$\sqrt{3}-3+\left(\pi +3\right)^{0}-\sqrt{2}+\sqrt{3}-21$$

Calculate \pi +3 to the power of 0 and get 1.

$$\sqrt{3}-3+1-\sqrt{2}+\sqrt{3}-21$$

Add -3 and 1 to get -2.

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

Combine \sqrt{3} and \sqrt{3} to get 2\sqrt{3}.

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

Subtract 21 from -2 to get -23.

$$2\sqrt{3}-23-\sqrt{2}$$