Solve frac{2sqrt{5}}{5}-frac{9sqrt{1}}{2}

$$\frac { 2 \sqrt { 5 } } { 5 } - \frac { 9 \sqrt { 1 } } { 2 }$$

Evaluate

$$\frac{2\sqrt{5}}{5}-\frac{9}{2}\approx -3.605572809$$

Short Solution Steps

Calculate the square root of 1 and get 1.

$$\frac{2\sqrt{5}}{5}-\frac{9\times 1}{2}$$

Multiply 9 and 1 to get 9.

$$\frac{2\sqrt{5}}{5}-\frac{9}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{2\sqrt{5}}{5} times \frac{2}{2}. Multiply \frac{9}{2} times \frac{5}{5}.

$$\frac{2\times 2\sqrt{5}}{10}-\frac{9\times 5}{10}$$

Since \frac{2\times 2\sqrt{5}}{10} and \frac{9\times 5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2\sqrt{5}-9\times 5}{10}$$

Do the multiplications in 2\times 2\sqrt{5}-9\times 5.

$$\frac{4\sqrt{5}-45}{10}$$

Factor

$$\frac{4 \sqrt{5} - 45}{10} = -3.6055728090000843$$