Solve frac{sqrt{70}}{3}*-frac{20sqrt{7}}{7}

$$\frac{ \sqrt{ 70 } }{ 3 } \times - \frac{ 20 \sqrt{ 7 } }{ 7 }$$

Evaluate

$$-\frac{20\sqrt{10}}{3}\approx -21.081851068$$

Solution Steps

Multiply \frac{\sqrt{70}}{3} times -\frac{20\sqrt{7}}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{70}\times 20\sqrt{7}}{3\times 7}$$

Factor 70=7\times 10. Rewrite the square root of the product \sqrt{7\times 10} as the product of square roots \sqrt{7}\sqrt{10}.

$$\frac{-\sqrt{7}\sqrt{10}\times 20\sqrt{7}}{3\times 7}$$

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

$$\frac{-7\times 20\sqrt{10}}{3\times 7}$$

Multiply -7 and 20 to get -140.

$$\frac{-140\sqrt{10}}{3\times 7}$$

Multiply 3 and 7 to get 21.

$$\frac{-140\sqrt{10}}{21}$$

Divide -140\sqrt{10} by 21 to get -\frac{20}{3}\sqrt{10}.

$$-\frac{20}{3}\sqrt{10}$$