Solve sqrt{5}+4div3-2sqrt{5}-2+sqrt{5}div4-2sqrt{5}

$$\sqrt{ 5 } +4 \div 3-2 \sqrt{ 5 } -2+ \sqrt{ 5 } \div 4-2 \sqrt{ 5 }$$

Evaluate

$$-\frac{11\sqrt{5}}{4}-\frac{2}{3}\approx -6.815853605$$

Solution Steps

Combine \sqrt{5} and -2\sqrt{5} to get -\sqrt{5}.

$$-\sqrt{5}+\frac{4}{3}-2+\frac{\sqrt{5}}{4}-2\sqrt{5}$$

Convert 2 to fraction \frac{6}{3}.

$$-\sqrt{5}+\frac{4}{3}-\frac{6}{3}+\frac{\sqrt{5}}{4}-2\sqrt{5}$$

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

$$-\sqrt{5}+\frac{4-6}{3}+\frac{\sqrt{5}}{4}-2\sqrt{5}$$

Subtract 6 from 4 to get -2.

$$-\sqrt{5}-\frac{2}{3}+\frac{\sqrt{5}}{4}-2\sqrt{5}$$

Combine -\sqrt{5} and \frac{\sqrt{5}}{4} to get -\frac{3}{4}\sqrt{5}.

$$-\frac{3}{4}\sqrt{5}-\frac{2}{3}-2\sqrt{5}$$

Combine -\frac{3}{4}\sqrt{5} and -2\sqrt{5} to get -\frac{11}{4}\sqrt{5}.

$$-\frac{11}{4}\sqrt{5}-\frac{2}{3}$$

Factor

$$\frac{-33 \sqrt{5} - 8}{12} = -6.815853604791088$$