Solve 15*sqrt{14}*3*sqrt{3}*sqrt{42}

$$15 \cdot \sqrt { 14 } \cdot 3 \cdot \sqrt { 3 } \cdot \sqrt { 42 }$$

Evaluate

$$1890$$

Solution Steps

Factor 42=14\times 3. Rewrite the square root of the product \sqrt{14\times 3} as the product of square roots \sqrt{14}\sqrt{3}.

$$3\times 15\sqrt{14}\sqrt{3}\sqrt{14}\sqrt{3}$$

Multiply \sqrt{14} and \sqrt{14} to get 14.

$$3\times 15\times 14\sqrt{3}\sqrt{3}$$

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

$$3\times 15\times 14\times 3$$

Multiply 3 and 15 to get 45.

$$45\times 14\times 3$$

Multiply 45 and 14 to get 630.

$$630\times 3$$

Multiply 630 and 3 to get 1890.

$$1890$$

Factor

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