Solve 3sqrt{8}div(-2sqrt{3}

$$3 \sqrt{ 8 } \div (-2 \sqrt{ 3 }$$

Evaluate

$$-\sqrt{6}\approx -2.449489743$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{3\times 2\sqrt{2}}{-2\sqrt{3}}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{2}}{-2\sqrt{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{2}}{-\sqrt{3}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-3\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of \frac{-3\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{-3\sqrt{2}\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{-3\sqrt{6}}{3}$$

Cancel out 3 and 3.

$$-\sqrt{6}$$