Solve 44+frac{sqrt{33}}{7}-frac{sqrt{66}}{6}

$$44 + \frac { \sqrt { 33 } } { 7 } - \frac { \sqrt { 66 } } { 6 }$$

Evaluate

$$\frac{\sqrt{33}}{7}-\frac{\sqrt{66}}{6}+44\approx 43.466645406$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 44 times \frac{7}{7}.

$$\frac{44\times 7}{7}+\frac{\sqrt{33}}{7}-\frac{\sqrt{66}}{6}$$

Since \frac{44\times 7}{7} and \frac{\sqrt{33}}{7} have the same denominator, add them by adding their numerators.

$$\frac{44\times 7+\sqrt{33}}{7}-\frac{\sqrt{66}}{6}$$

Do the multiplications in 44\times 7+\sqrt{33}.

$$\frac{308+\sqrt{33}}{7}-\frac{\sqrt{66}}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 6 is 42. Multiply \frac{308+\sqrt{33}}{7} times \frac{6}{6}. Multiply \frac{\sqrt{66}}{6} times \frac{7}{7}.

$$\frac{6\left(308+\sqrt{33}\right)}{42}-\frac{7\sqrt{66}}{42}$$

Since \frac{6\left(308+\sqrt{33}\right)}{42} and \frac{7\sqrt{66}}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\left(308+\sqrt{33}\right)-7\sqrt{66}}{42}$$

Do the multiplications in 6\left(308+\sqrt{33}\right)-7\sqrt{66}.

$$\frac{1848+6\sqrt{33}-7\sqrt{66}}{42}$$

Factor

$$\frac{6 \sqrt{33} + 1848 - 7 \sqrt{66}}{42} = 43.46664540587563$$