Solve frac{sqrt{10}}{2}div2sqrt{7}*frac{-20sqrt{7}}{7}

$$\frac { \sqrt { 10 } } { 2 } \div 2 \sqrt { 7 } \times \frac { - 20 \sqrt { 7 } } { 7 }$$

Evaluate

$$-5\sqrt{10}\approx -15.811388301$$

Solution Steps

Express \frac{\frac{\sqrt{10}}{2}}{2} as a single fraction.

$$\frac{\sqrt{10}}{2\times 2}\sqrt{7}\times \frac{-20\sqrt{7}}{7}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{10}}{4}\sqrt{7}\times \frac{-20\sqrt{7}}{7}$$

Express \frac{\sqrt{10}}{4}\sqrt{7} as a single fraction.

$$\frac{\sqrt{10}\sqrt{7}}{4}\times \frac{-20\sqrt{7}}{7}$$

Multiply \frac{\sqrt{10}\sqrt{7}}{4} times \frac{-20\sqrt{7}}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{10}\sqrt{7}\left(-20\right)\sqrt{7}}{4\times 7}$$

Cancel out 4 in both numerator and denominator.

$$\frac{-5\sqrt{7}\sqrt{7}\sqrt{10}}{7}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{-5\times 7\sqrt{10}}{7}$$

Cancel out 7 and 7.

$$-5\sqrt{10}$$