Solve frac{-sqrt{56}}{2sqrt{14}}

$$\frac { - \sqrt { 56 } } { 2 \sqrt { 14 } }$$

Evaluate

$$-1$$

Solution Steps

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\frac{-2\sqrt{14}}{2\sqrt{14}}$$

Rationalize the denominator of \frac{-2\sqrt{14}}{2\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{\left(-2\sqrt{14}\right)\sqrt{14}}{2\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{\left(-2\sqrt{14}\right)\sqrt{14}}{2\times 14}$$

Multiply 2 and 14 to get 28.

$$\frac{\left(-2\sqrt{14}\right)\sqrt{14}}{28}$$

Multiply -1 and 2 to get -2.

$$\frac{-2\sqrt{14}\sqrt{14}}{28}$$

Multiply \sqrt{14} and \sqrt{14} to get 14.

$$\frac{-2\times 14}{28}$$

Multiply -2 and 14 to get -28.

$$\frac{-28}{28}$$

Divide -28 by 28 to get -1.

$$-1$$

Factor

$$-1$$