Solve frac{-20sqrt{12}}{2sqrt{2}}

$$\frac{ -20 \sqrt{ 12 } }{ 2 \sqrt{ 2 } }$$

Evaluate

$$-10\sqrt{6}\approx -24.494897428$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{-10\sqrt{12}}{\sqrt{2}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{-10\times 2\sqrt{3}}{\sqrt{2}}$$

Multiply -10 and 2 to get -20.

$$\frac{-20\sqrt{3}}{\sqrt{2}}$$

Rationalize the denominator of \frac{-20\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-20\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-20\sqrt{3}\sqrt{2}}{2}$$

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

$$\frac{-20\sqrt{6}}{2}$$

Divide -20\sqrt{6} by 2 to get -10\sqrt{6}.

$$-10\sqrt{6}$$