Solve 4/20+frac{2{5}}*sqrt{5}+9

$$\frac{ 4 }{ 20+ \frac{ 2 }{ 5 } } \times \sqrt{ 5 } +9$$

Evaluate

$$\frac{10\sqrt{5}}{51}+9\approx 9.438444701$$

Solution Steps

Convert 20 to fraction \frac{100}{5}.

$$\frac{4}{\frac{100}{5}+\frac{2}{5}}\sqrt{5}+9$$

Since \frac{100}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\frac{4}{\frac{100+2}{5}}\sqrt{5}+9$$

Add 100 and 2 to get 102.

$$\frac{4}{\frac{102}{5}}\sqrt{5}+9$$

Divide 4 by \frac{102}{5} by multiplying 4 by the reciprocal of \frac{102}{5}.

$$4\times \frac{5}{102}\sqrt{5}+9$$

Express 4\times \frac{5}{102} as a single fraction.

$$\frac{4\times 5}{102}\sqrt{5}+9$$

Multiply 4 and 5 to get 20.

$$\frac{20}{102}\sqrt{5}+9$$

Reduce the fraction \frac{20}{102} to lowest terms by extracting and canceling out 2.

$$\frac{10}{51}\sqrt{5}+9$$