Solve frac{10^2+10^2-frac{sqrt{3}}{2}}{200}

$$\frac { 10 ^ { 2 } + 10 ^ { 2 } - \frac { \sqrt { 3 } } { 2 } } { 200 }$$

Evaluate

$$-\frac{\sqrt{3}}{400}+1\approx 0.995669873$$

Short Solution Steps

Calculate 10 to the power of 2 and get 100.

$$\frac{100+10^{2}-\frac{\sqrt{3}}{2}}{200}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{100+100-\frac{\sqrt{3}}{2}}{200}$$

Add 100 and 100 to get 200.

$$\frac{200-\frac{\sqrt{3}}{2}}{200}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 200 times \frac{2}{2}.

$$\frac{\frac{200\times 2}{2}-\frac{\sqrt{3}}{2}}{200}$$

Since \frac{200\times 2}{2} and \frac{\sqrt{3}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{200\times 2-\sqrt{3}}{2}}{200}$$

Do the multiplications in 200\times 2-\sqrt{3}.

$$\frac{\frac{400-\sqrt{3}}{2}}{200}$$

Express \frac{\frac{400-\sqrt{3}}{2}}{200} as a single fraction.

$$\frac{400-\sqrt{3}}{2\times 200}$$

Multiply 2 and 200 to get 400.

$$\frac{400-\sqrt{3}}{400}$$

Factor

$$\frac{400 - \sqrt{3}}{400} = 0.9956698729810778$$