Solve 3/2-(2-5*sqrt{125})div10

$$\frac { 3 } { 2 } - ( 2 - 5 \cdot \sqrt { 125 } ) \div 10$$

Evaluate

$$\frac{5\sqrt{5}}{2}+\frac{13}{10}\approx 6.890169944$$

Short Solution Steps

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

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

Multiply -5 and 5 to get -25.

$$\frac{3}{2}-\frac{2-25\sqrt{5}}{10}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 10 is 10. Multiply \frac{3}{2} times \frac{5}{5}.

$$\frac{3\times 5}{10}-\frac{2-25\sqrt{5}}{10}$$

Since \frac{3\times 5}{10} and \frac{2-25\sqrt{5}}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 5-\left(2-25\sqrt{5}\right)}{10}$$

Do the multiplications in 3\times 5-\left(2-25\sqrt{5}\right).

$$\frac{15-2+25\sqrt{5}}{10}$$

Do the calculations in 15-2+25\sqrt{5}.

$$\frac{13+25\sqrt{5}}{10}$$

Factor

$$\frac{25 \sqrt{5} + 13}{10} = 6.890169943749474$$