Solve 3sqrt{10}x7sqrt{14}*sqrt{5}

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

Evaluate

$$30\sqrt{7}x_{7}$$

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}.

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

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

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

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}.

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

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

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

Multiply 3 and 5 to get 15.

$$15x_{7}\times 2\sqrt{7}$$

Multiply 15 and 2 to get 30.

$$30x_{7}\sqrt{7}$$

Differentiate w.r.t. x_7

$$30 \sqrt{7} = 79.372539332$$