Solve 4/sqrt{5}+1/3sqrt{5}-1/4sqrt{20}-3/20

$$\frac { 4 } { \sqrt { 5 } } + \frac { 1 } { 3 } \sqrt { 5 } - \frac { 1 } { 4 } \sqrt { 20 } - \frac { 3 } { 20 }$$

Evaluate

$$\frac{19\sqrt{5}}{30}-\frac{3}{20}\approx 1.266176386$$

Solution Steps

Rationalize the denominator of \frac{4}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{4\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+\frac{1}{3}\sqrt{5}-\frac{1}{4}\sqrt{20}-\frac{3}{20}$$

The square of \sqrt{5} is 5.

$$\frac{4\sqrt{5}}{5}+\frac{1}{3}\sqrt{5}-\frac{1}{4}\sqrt{20}-\frac{3}{20}$$

Combine \frac{4\sqrt{5}}{5} and \frac{1}{3}\sqrt{5} to get \frac{17}{15}\sqrt{5}.

$$\frac{17}{15}\sqrt{5}-\frac{1}{4}\sqrt{20}-\frac{3}{20}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{17}{15}\sqrt{5}-\frac{1}{4}\times 2\sqrt{5}-\frac{3}{20}$$

Express -\frac{1}{4}\times 2 as a single fraction.

$$\frac{17}{15}\sqrt{5}+\frac{-2}{4}\sqrt{5}-\frac{3}{20}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{17}{15}\sqrt{5}-\frac{1}{2}\sqrt{5}-\frac{3}{20}$$

Combine \frac{17}{15}\sqrt{5} and -\frac{1}{2}\sqrt{5} to get \frac{19}{30}\sqrt{5}.

$$\frac{19}{30}\sqrt{5}-\frac{3}{20}$$

Factor

$$\frac{38 \sqrt{5} - 9}{60} = 1.266176385749867$$