Solve 19sqrt{7}*2sqrt{6}*sqrt{42}

$$19 \sqrt { 7 } \cdot 2 \sqrt { 6 } \cdot \sqrt { 42 }$$

Evaluate

$$1596$$

Solution Steps

Factor 42=7\times 6. Rewrite the square root of the product \sqrt{7\times 6} as the product of square roots \sqrt{7}\sqrt{6}.

$$2\times 19\sqrt{7}\sqrt{6}\sqrt{7}\sqrt{6}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$2\times 19\times 7\sqrt{6}\sqrt{6}$$

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

$$2\times 19\times 7\times 6$$

Multiply 2 and 19 to get 38.

$$38\times 7\times 6$$

Multiply 38 and 7 to get 266.

$$266\times 6$$

Multiply 266 and 6 to get 1596.

$$1596$$

Factor

$$2^{2}\times 3\times 7\times 19$$