Solve frac{6^2sqrt[3]{-125}}{sqrt{10}}

$$\frac{ { 6 }^{ 2 } \sqrt[ 3 ]{ -125 } }{ \sqrt{ 10 } }$$

Evaluate

$$-18\sqrt{10}\approx -56.920997883$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\frac{36\sqrt[3]{-125}}{\sqrt{10}}$$

Calculate \sqrt[3]{-125} and get -5.

$$\frac{36\left(-5\right)}{\sqrt{10}}$$

Multiply 36 and -5 to get -180.

$$\frac{-180}{\sqrt{10}}$$

Rationalize the denominator of \frac{-180}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{-180\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{-180\sqrt{10}}{10}$$

Divide -180\sqrt{10} by 10 to get -18\sqrt{10}.

$$-18\sqrt{10}$$