Solve 10sqrt{7}*2sqrt{6}*sqrt{42}=

$$10 \sqrt { 7 } \cdot 2 \sqrt { 6 } \cdot \sqrt { 42 } =$$

Evaluate

$$840$$

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}.

$$2\times 10\sqrt{7}\sqrt{6}\sqrt{7}\sqrt{6}$$

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

$$2\times 10\times 7\sqrt{6}\sqrt{6}$$

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

$$2\times 10\times 7\times 6$$

Multiply 2 and 10 to get 20.

$$20\times 7\times 6$$

Multiply 20 and 7 to get 140.

$$140\times 6$$

Multiply 140 and 6 to get 840.

$$840$$

Factor

$$2^{3}\times 3\times 5\times 7$$