Solve (2-3sqrt{2})divsqrt{2}

$$( 2 - 3 \sqrt { 2 } ) \div \sqrt { 2 }$$

Evaluate

$$\sqrt{2}-3\approx -1.585786438$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

The square of \sqrt{2} is 2.

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

Multiply -3 and 2 to get -6.

$$\frac{2\sqrt{2}-6}{2}$$

Divide each term of 2\sqrt{2}-6 by 2 to get \sqrt{2}-3.

$$\sqrt{2}-3$$

Factor

$$\sqrt{2} - 3 = -1.585786438$$