Solve 6sqrt{7}*1/2*frac{6-sqrt{7}}{6}

$$6 \sqrt { 7 } \times \frac { 1 } { 2 } \times \frac { 6 - \sqrt { 7 } } { 6 }$$

Evaluate

$$3\sqrt{7}-\frac{7}{2}\approx 4.437253933$$

Solution Steps

Multiply 6 and \frac{1}{2} to get \frac{6}{2}.

$$\frac{6}{2}\sqrt{7}\times \frac{6-\sqrt{7}}{6}$$

Divide 6 by 2 to get 3.

$$3\sqrt{7}\times \frac{6-\sqrt{7}}{6}$$

Cancel out 6, the greatest common factor in 3 and 6.

$$\frac{6-\sqrt{7}}{2}\sqrt{7}$$

Express \frac{6-\sqrt{7}}{2}\sqrt{7} as a single fraction.

$$\frac{\left(6-\sqrt{7}\right)\sqrt{7}}{2}$$

Use the distributive property to multiply 6-\sqrt{7} by \sqrt{7}.

$$\frac{6\sqrt{7}-\left(\sqrt{7}\right)^{2}}{2}$$

The square of \sqrt{7} is 7.

$$\frac{6\sqrt{7}-7}{2}$$