Solve frac{sqrt{2}*(-8sqrt{15})*sqrt{2}}{-2sqrt{5}}

$$\frac{ \sqrt{ 2 } \times (-8 \sqrt{ 15 } ) \times \sqrt{ 2 } }{ -2 \sqrt{ 5 } }$$

Evaluate

$$8\sqrt{3}\approx 13.856406461$$

Solution Steps

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{2\left(-8\right)\sqrt{15}}{-2\sqrt{5}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-8\sqrt{15}}{-\sqrt{5}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{8\sqrt{15}}{\sqrt{5}}$$

Rationalize the denominator of \frac{8\sqrt{15}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{8\sqrt{15}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{8\sqrt{15}\sqrt{5}}{5}$$

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

$$\frac{8\sqrt{5}\sqrt{3}\sqrt{5}}{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{8\times 5\sqrt{3}}{5}$$

Cancel out 5 and 5.

$$8\sqrt{3}$$