Solve 2-frac{3+sqrt{4}-sqrt{2}}{2sqrt{2}}

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

Evaluate

$$-\frac{5\sqrt{2}}{4}+\frac{5}{2}\approx 0.732233047$$

Short Solution Steps

Calculate the square root of 4 and get 2.

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

Add 3 and 2 to get 5.

$$2-\frac{5-\sqrt{2}}{2\sqrt{2}}$$

Rationalize the denominator of \frac{5-\sqrt{2}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$2-\frac{\left(5-\sqrt{2}\right)\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$2-\frac{\left(5-\sqrt{2}\right)\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$2-\frac{\left(5-\sqrt{2}\right)\sqrt{2}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{4}{4}.

$$\frac{2\times 4}{4}-\frac{\left(5-\sqrt{2}\right)\sqrt{2}}{4}$$

Since \frac{2\times 4}{4} and \frac{\left(5-\sqrt{2}\right)\sqrt{2}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 4-\left(5-\sqrt{2}\right)\sqrt{2}}{4}$$

Do the multiplications in 2\times 4-\left(5-\sqrt{2}\right)\sqrt{2}.

$$\frac{8-5\sqrt{2}+2}{4}$$

Do the calculations in 8-5\sqrt{2}+2.

$$\frac{10-5\sqrt{2}}{4}$$

Factor

$$\frac{5 \sqrt{2} {(\sqrt{2} - 1)}}{4} = 0.7322330470336313$$