Solve 2sqrt{2}+(2-3/4)-2[3/3-3/2*2](1/2)]

$$2 \sqrt { 2 } + ( \frac { 2 - 3 } { 4 } ) - 2 [ \frac { 3 } { 3 } - \frac { 3 } { 2 } \cdot 2 ] ( \frac { 1 } { 2 } ) ]$$

Evaluate

$$2\sqrt{2}+\frac{7}{4}\approx 4.578427125$$

Solution Steps

Divide 3 by 3 to get 1.

$$2\sqrt{2}+\frac{2-3}{4}-2\left(1-\frac{3}{2}\times 2\right)\times \frac{1}{2}$$

Subtract 3 from 2 to get -1.

$$2\sqrt{2}+\frac{-1}{4}-2\left(1-\frac{3}{2}\times 2\right)\times \frac{1}{2}$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$2\sqrt{2}-\frac{1}{4}-2\left(1-\frac{3}{2}\times 2\right)\times \frac{1}{2}$$

Cancel out 2 and 2.

$$2\sqrt{2}-\frac{1}{4}-2\left(1-3\right)\times \frac{1}{2}$$

Subtract 3 from 1 to get -2.

$$2\sqrt{2}-\frac{1}{4}-2\left(-2\right)\times \frac{1}{2}$$

Multiply 2 and -2 to get -4.

$$2\sqrt{2}-\frac{1}{4}-\left(-4\times \frac{1}{2}\right)$$

Multiply -4 and \frac{1}{2} to get \frac{-4}{2}.

$$2\sqrt{2}-\frac{1}{4}-\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$2\sqrt{2}-\frac{1}{4}-\left(-2\right)$$

The opposite of -2 is 2.

$$2\sqrt{2}-\frac{1}{4}+2$$

Convert 2 to fraction \frac{8}{4}.

$$2\sqrt{2}-\frac{1}{4}+\frac{8}{4}$$

Since -\frac{1}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$2\sqrt{2}+\frac{-1+8}{4}$$

Add -1 and 8 to get 7.

$$2\sqrt{2}+\frac{7}{4}$$

Factor

$$\frac{8 \sqrt{2} + 7}{4} = 4.57842712474619$$