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

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

Evaluate

$$\sqrt{6}-1\approx 1.449489743$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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

The square of \sqrt{2} is 2.

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

Divide each term of 2\sqrt{6}-2 by 2 to get \sqrt{6}-1.

$$\sqrt{6}-1$$

Factor

$$\sqrt{6} - 1 = 1.449489743$$