Solve 441/2left(22/21-frac{sqrt{3}}{2}right)

$$\frac{ 441 }{ 2 } \left( \frac{ 22 }{ 21 } - \frac{ \sqrt{ 3 } }{ 2 } \right)$$

Evaluate

$$-\frac{441\sqrt{3}}{4}+231\approx 40.041398466$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 21 and 2 is 42. Multiply \frac{22}{21} times \frac{2}{2}. Multiply \frac{\sqrt{3}}{2} times \frac{21}{21}.

$$\frac{441}{2}\left(\frac{22\times 2}{42}-\frac{21\sqrt{3}}{42}\right)$$

Since \frac{22\times 2}{42} and \frac{21\sqrt{3}}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{441}{2}\times \frac{22\times 2-21\sqrt{3}}{42}$$

Do the multiplications in 22\times 2-21\sqrt{3}.

$$\frac{441}{2}\times \frac{44-21\sqrt{3}}{42}$$

Multiply \frac{441}{2} times \frac{44-21\sqrt{3}}{42} by multiplying numerator times numerator and denominator times denominator.

$$\frac{441\left(44-21\sqrt{3}\right)}{2\times 42}$$

Cancel out 21 in both numerator and denominator.

$$\frac{21\left(-21\sqrt{3}+44\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{21\left(-21\sqrt{3}+44\right)}{4}$$

Use the distributive property to multiply 21 by -21\sqrt{3}+44.

$$\frac{-441\sqrt{3}+924}{4}$$

Factor

$$\frac{21 {(44 - 21 \sqrt{3})}}{4} = 40.04139846553127$$