Solve v-36/sqrt{2}sqrt{-9}

$$\frac { v - 36 } { \sqrt { 2 } } \sqrt { - 9 }$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Rationalize the denominator of \frac{v-36}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(v-36\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\sqrt{-9}$$

The square of \sqrt{2} is 2.

$$\frac{\left(v-36\right)\sqrt{2}}{2}\sqrt{-9}$$

Express \frac{\left(v-36\right)\sqrt{2}}{2}\sqrt{-9} as a single fraction.

$$\frac{\left(v-36\right)\sqrt{2}\sqrt{-9}}{2}$$

Use the distributive property to multiply v-36 by \sqrt{2}.

$$\frac{\left(v\sqrt{2}-36\sqrt{2}\right)\sqrt{-9}}{2}$$

Use the distributive property to multiply v\sqrt{2}-36\sqrt{2} by \sqrt{-9}.

$$\frac{v\sqrt{2}\sqrt{-9}-36\sqrt{2}\sqrt{-9}}{2}$$

Evaluate (complex solution)

$$\frac{3\sqrt{2}i\left(v-36\right)}{2}$$