Solve sqrt{17/4-2}-sqrt{281/16-4}

$$\sqrt { \frac { 17 } { 4 } - 2 } - \sqrt { \frac { 281 } { 16 } - 4 }$$

Evaluate

$$-\frac{\sqrt{217}}{4}+\frac{3}{2}\approx -2.182729966$$

Short Solution Steps

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

$$\sqrt{\frac{17}{4}-\frac{8}{4}}-\sqrt{\frac{281}{16}-4}$$

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

$$\sqrt{\frac{17-8}{4}}-\sqrt{\frac{281}{16}-4}$$

Subtract 8 from 17 to get 9.

$$\sqrt{\frac{9}{4}}-\sqrt{\frac{281}{16}-4}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{3}{2}-\sqrt{\frac{281}{16}-4}$$

Convert 4 to fraction \frac{64}{16}.

$$\frac{3}{2}-\sqrt{\frac{281}{16}-\frac{64}{16}}$$

Since \frac{281}{16} and \frac{64}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}-\sqrt{\frac{281-64}{16}}$$

Subtract 64 from 281 to get 217.

$$\frac{3}{2}-\sqrt{\frac{217}{16}}$$

Rewrite the square root of the division \sqrt{\frac{217}{16}} as the division of square roots \frac{\sqrt{217}}{\sqrt{16}}.

$$\frac{3}{2}-\frac{\sqrt{217}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$\frac{3}{2}-\frac{\sqrt{217}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{3}{2} times \frac{2}{2}.

$$\frac{3\times 2}{4}-\frac{\sqrt{217}}{4}$$

Since \frac{3\times 2}{4} and \frac{\sqrt{217}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 2-\sqrt{217}}{4}$$

Do the multiplications in 3\times 2-\sqrt{217}.

$$\frac{6-\sqrt{217}}{4}$$

Factor

$$\frac{6 - \sqrt{217}}{4} = -2.1827299656640586$$