Solve frac{-sqrt{48}}{sqrt{3}}

$$\frac { - \sqrt { 48 } } { \sqrt { 3 } }$$

Evaluate

$$-4$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

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

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

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

The square of \sqrt{3} is 3.

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

Multiply -1 and 4 to get -4.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{-4\times 3}{3}$$

Multiply -4 and 3 to get -12.

$$\frac{-12}{3}$$

Divide -12 by 3 to get -4.

$$-4$$

Factor

$$-4$$