Solve 9+18-36/2*3sqrt{2*3}

$$\frac{ 9+18-36 }{ 2 \cdot 3 \sqrt{ 2 } \times 3 }$$

Evaluate

$$-\frac{\sqrt{2}}{4}\approx -0.353553391$$

Solution Steps

Add 9 and 18 to get 27.

$$\frac{27-36}{2\times 3\times 3\sqrt{2}}$$

Subtract 36 from 27 to get -9.

$$\frac{-9}{2\times 3\times 3\sqrt{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{-9}{6\times 3\sqrt{2}}$$

Multiply 6 and 3 to get 18.

$$\frac{-9}{18\sqrt{2}}$$

Rationalize the denominator of \frac{-9}{18\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-9\sqrt{2}}{18\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-9\sqrt{2}}{18\times 2}$$

Cancel out 9 in both numerator and denominator.

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

Multiply 2 and 2 to get 4.

$$\frac{-\sqrt{2}}{4}$$