Solve 2sqrt{14}*sqrt{21}*sqrt{3}

$$2 \sqrt { 14 } \cdot \sqrt { 21 } \cdot \sqrt { 3 }$$

Evaluate

$$42\sqrt{2}\approx 59.39696962$$

Solution Steps

Factor 21=3\times 7. Rewrite the square root of the product \sqrt{3\times 7} as the product of square roots \sqrt{3}\sqrt{7}.

$$2\sqrt{14}\sqrt{3}\sqrt{7}\sqrt{3}$$

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

$$2\sqrt{14}\times 3\sqrt{7}$$

Factor 14=7\times 2. Rewrite the square root of the product \sqrt{7\times 2} as the product of square roots \sqrt{7}\sqrt{2}.

$$2\sqrt{7}\sqrt{2}\times 3\sqrt{7}$$

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

$$2\times 7\times 3\sqrt{2}$$

Multiply 2 and 7 to get 14.

$$14\times 3\sqrt{2}$$

Multiply 14 and 3 to get 42.

$$42\sqrt{2}$$