Solve =frac{-3+6sqrt{2}}{2sqrt{2}}

$$= \frac { - 3 + 6 \sqrt { 2 } } { 2 \sqrt { 2 } }$$

Evaluate

$$-\frac{3\sqrt{2}}{4}+3\approx 1.939339828$$

Solution Steps

Rationalize the denominator of \frac{-3+6\sqrt{2}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

$$\frac{\left(-3+6\sqrt{2}\right)\sqrt{2}}{4}$$

Use the distributive property to multiply -3+6\sqrt{2} by \sqrt{2}.

$$\frac{-3\sqrt{2}+6\left(\sqrt{2}\right)^{2}}{4}$$

The square of \sqrt{2} is 2.

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

Multiply 6 and 2 to get 12.

$$\frac{-3\sqrt{2}+12}{4}$$

Factor

$$\frac{3 {(4 - \sqrt{2})}}{4} = 1.9393398282201788$$