Solve {c}{frac{sqrt{42}}{28}*(-5)}{*frac{sqrt{112}}{7}}

$$\left. \begin{array} { c } { \frac { \sqrt { 42 } } { 28 } \times ( - 5 ) } \\ { \times \frac { \sqrt { 112 } } { 7 } } \end{array} \right.$$

Evaluate

$$-\frac{5\sqrt{6}}{7}\approx -1.749635531$$

Solution Steps

Factor 112=4^{2}\times 7. Rewrite the square root of the product \sqrt{4^{2}\times 7} as the product of square roots \sqrt{4^{2}}\sqrt{7}. Take the square root of 4^{2}.

$$\frac{\sqrt{42}}{28}\left(-5\right)\times \frac{4\sqrt{7}}{7}$$

Express \frac{\sqrt{42}}{28}\left(-5\right) as a single fraction.

$$\frac{-\sqrt{42}\times 5}{28}\times \frac{4\sqrt{7}}{7}$$

Multiply \frac{-\sqrt{42}\times 5}{28} times \frac{4\sqrt{7}}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{42}\times 5\times 4\sqrt{7}}{28\times 7}$$

Cancel out 4 in both numerator and denominator.

$$\frac{-5\sqrt{7}\sqrt{42}}{7\times 7}$$

Factor 42=7\times 6. Rewrite the square root of the product \sqrt{7\times 6} as the product of square roots \sqrt{7}\sqrt{6}.

$$\frac{-5\sqrt{7}\sqrt{7}\sqrt{6}}{7\times 7}$$

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

$$\frac{-5\times 7\sqrt{6}}{7\times 7}$$

Multiply -5 and 7 to get -35.

$$\frac{-35\sqrt{6}}{7\times 7}$$

Multiply 7 and 7 to get 49.

$$\frac{-35\sqrt{6}}{49}$$

Divide -35\sqrt{6} by 49 to get -\frac{5}{7}\sqrt{6}.

$$-\frac{5}{7}\sqrt{6}$$