Solve 3sqrt{10}*7sqrt{14}*sqrt{5}

$$3 \sqrt{ 10 } \times 7 \sqrt{ 14 } \times \sqrt{ 5 }$$

Evaluate

$$210\sqrt{7}\approx 555.607775324$$

Solution Steps

Factor 10=5\times 2. Rewrite the square root of the product \sqrt{5\times 2} as the product of square roots \sqrt{5}\sqrt{2}.

$$3\times 7\sqrt{5}\sqrt{2}\sqrt{14}\sqrt{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$3\times 7\times 5\sqrt{14}\sqrt{2}$$

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

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 3 and 7 to get 21.

$$21\times 5\times 2\sqrt{7}$$

Multiply 21 and 5 to get 105.

$$105\times 2\sqrt{7}$$

Multiply 105 and 2 to get 210.

$$210\sqrt{7}$$