Solve sqrt{1/4+4+2}-sqrt{4+4-2}=

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

Evaluate

$$\frac{5}{2}-\sqrt{6}\approx 0.050510257$$

Solution Steps

Convert 4 to fraction \frac{16}{4}.

$$\sqrt{\frac{1}{4}+\frac{16}{4}+2}-\sqrt{4+4-2}$$

Since \frac{1}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{1+16}{4}+2}-\sqrt{4+4-2}$$

Add 1 and 16 to get 17.

$$\sqrt{\frac{17}{4}+2}-\sqrt{4+4-2}$$

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

$$\sqrt{\frac{17}{4}+\frac{8}{4}}-\sqrt{4+4-2}$$

Since \frac{17}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{17+8}{4}}-\sqrt{4+4-2}$$

Add 17 and 8 to get 25.

$$\sqrt{\frac{25}{4}}-\sqrt{4+4-2}$$

Rewrite the square root of the division \frac{25}{4} as the division of square roots \frac{\sqrt{25}}{\sqrt{4}}. Take the square root of both numerator and denominator.

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

Add 4 and 4 to get 8.

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

Subtract 2 from 8 to get 6.

$$\frac{5}{2}-\sqrt{6}$$

Factor

$$\frac{5 - 2 \sqrt{6}}{2} = 0.05051025721682212$$