Solve frac{-sqrt{80}}{4sqrt{3}}

$$\frac { - \sqrt { 80 } } { 4 \sqrt { 3 } }$$

Evaluate

$$-\frac{\sqrt{15}}{3}\approx -1.290994449$$

Solution Steps

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{-4\sqrt{5}}{4\sqrt{3}}$$

Rationalize the denominator of \frac{-4\sqrt{5}}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(-4\sqrt{5}\right)\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(-4\sqrt{5}\right)\sqrt{3}}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{\left(-4\sqrt{5}\right)\sqrt{3}}{12}$$

Multiply -1 and 4 to get -4.

$$\frac{-4\sqrt{5}\sqrt{3}}{12}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{-4\sqrt{15}}{12}$$

Divide -4\sqrt{15} by 12 to get -\frac{1}{3}\sqrt{15}.

$$-\frac{1}{3}\sqrt{15}$$