Solve frac{sqrt{4}+sqrt{2(1/2)}}{2}-sqrt{3(frac{1/3)}+sqrt{8(1/2)}}{4}

$$\frac { \sqrt { 4 } + \sqrt { 2 ( \frac { 1 } { 2 } ) } } { 2 } - \frac { \sqrt { 3 ( \frac { 1 } { 3 } ) } + \sqrt { 8 ( \frac { 1 } { 2 } ) } } { 4 }$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{2+\sqrt{2\times \frac{1}{2}}}{2}-\frac{\sqrt{3\times \frac{1}{3}}+\sqrt{8\times \frac{1}{2}}}{4}$$

Cancel out 2 and 2.

$$\frac{2+\sqrt{1}}{2}-\frac{\sqrt{3\times \frac{1}{3}}+\sqrt{8\times \frac{1}{2}}}{4}$$

Calculate the square root of 1 and get 1.

$$\frac{2+1}{2}-\frac{\sqrt{3\times \frac{1}{3}}+\sqrt{8\times \frac{1}{2}}}{4}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}-\frac{\sqrt{3\times \frac{1}{3}}+\sqrt{8\times \frac{1}{2}}}{4}$$

Cancel out 3 and 3.

$$\frac{3}{2}-\frac{\sqrt{1}+\sqrt{8\times \frac{1}{2}}}{4}$$

Calculate the square root of 1 and get 1.

$$\frac{3}{2}-\frac{1+\sqrt{8\times \frac{1}{2}}}{4}$$

Multiply 8 and \frac{1}{2} to get \frac{8}{2}.

$$\frac{3}{2}-\frac{1+\sqrt{\frac{8}{2}}}{4}$$

Divide 8 by 2 to get 4.

$$\frac{3}{2}-\frac{1+\sqrt{4}}{4}$$

Calculate the square root of 4 and get 2.

$$\frac{3}{2}-\frac{1+2}{4}$$

Add 1 and 2 to get 3.

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

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{6}{4}-\frac{3}{4}$$

Since \frac{6}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-3}{4}$$

Subtract 3 from 6 to get 3.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$