Solve 4-(4-frac{5sqrt{2}}{2})

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

Evaluate

$$\frac{5\sqrt{2}}{2}\approx 3.535533906$$

Short Solution Steps

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

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

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

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

Do the multiplications in 4\times 2-5\sqrt{2}.

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

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

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

Since \frac{4\times 2}{2} and \frac{8-5\sqrt{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\times 2-\left(8-5\sqrt{2}\right)}{2}$$

Do the multiplications in 4\times 2-\left(8-5\sqrt{2}\right).

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

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

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