Solve 2sqrt{5}-frac{7-3sqrt{10}}{2}

$$2 \sqrt { 5 } - \frac { 7 - 3 \sqrt { 10 } } { 2 }$$

Evaluate

$$\frac{3\sqrt{10}}{2}+2\sqrt{5}-\frac{7}{2}\approx 5.715552445$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 2\sqrt{5} times \frac{2}{2}.

$$\frac{2\times 2\sqrt{5}}{2}-\frac{7-3\sqrt{10}}{2}$$

Since \frac{2\times 2\sqrt{5}}{2} and \frac{7-3\sqrt{10}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2\sqrt{5}-\left(7-3\sqrt{10}\right)}{2}$$

Do the multiplications in 2\times 2\sqrt{5}-\left(7-3\sqrt{10}\right).

$$\frac{4\sqrt{5}-7+3\sqrt{10}}{2}$$

Factor

$$\frac{3 \sqrt{10} + 4 \sqrt{5} - 7}{2} = 5.715552445252149$$