Solve 5sqrt{13}*4sqrt{3}*sqrt{39}

$$5 \sqrt { 13 } \cdot 4 \sqrt { 3 } \cdot \sqrt { 39 }$$

Evaluate

$$780$$

Solution Steps

Factor 39=13\times 3. Rewrite the square root of the product \sqrt{13\times 3} as the product of square roots \sqrt{13}\sqrt{3}.

$$4\times 5\sqrt{13}\sqrt{3}\sqrt{13}\sqrt{3}$$

Multiply \sqrt{13} and \sqrt{13} to get 13.

$$4\times 5\times 13\sqrt{3}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$4\times 5\times 13\times 3$$

Multiply 4 and 5 to get 20.

$$20\times 13\times 3$$

Multiply 20 and 13 to get 260.

$$260\times 3$$

Multiply 260 and 3 to get 780.

$$780$$

Factor

$$2^{2}\times 3\times 5\times 13$$