Solve sqrt[3]{sqrt{72}*sqrt{648}}

$$\sqrt[ 3 ] { \sqrt { 72 } \cdot \sqrt { 648 } }$$

Evaluate

$$6$$

Solution Steps

Factor 648=72\times 9. Rewrite the square root of the product \sqrt{72\times 9} as the product of square roots \sqrt{72}\sqrt{9}.

$$\sqrt[3]{\sqrt{72}\sqrt{72}\sqrt{9}}$$

Multiply \sqrt{72} and \sqrt{72} to get 72.

$$\sqrt[3]{72\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\sqrt[3]{72\times 3}$$

Multiply 72 and 3 to get 216.

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

Calculate \sqrt[3]{216} and get 6.

$$6$$

Factor

$$2\times 3$$