Solve sqrt{6^3}*sqrt[3]{6}:sqrt{6}=

$$\sqrt { 6 ^ { 3 } } \cdot \sqrt[ 3 ] { 6 } : \sqrt { 6 } =$$

Evaluate

$$6^{\frac{4}{3}}\approx 10.902723557$$

Solution Steps

Calculate 6 to the power of 3 and get 216.

$$\frac{\sqrt{216}\sqrt[3]{6}}{\sqrt{6}}$$

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$\frac{6\sqrt{6}\sqrt[3]{6}}{\sqrt{6}}$$

Rationalize the denominator of \frac{6\sqrt{6}\sqrt[3]{6}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{6\sqrt{6}\sqrt[3]{6}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{6\sqrt{6}\sqrt[3]{6}\sqrt{6}}{6}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{6\times 6\sqrt[3]{6}}{6}$$

Multiply 6 and 6 to get 36.

$$\frac{36\sqrt[3]{6}}{6}$$

Divide 36\sqrt[3]{6} by 6 to get 6\sqrt[3]{6}.

$$6\sqrt[3]{6}$$