Solve x*25div6^2sqrt{2*6^2}

$$x \times 25 \div { 6 }^{ 2 } \sqrt{ 2 \times { 6 }^{ 2 } }$$

Evaluate

$$\frac{25\sqrt{2}x}{6}$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\frac{x\times 25}{36}\sqrt{2\times 6^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{x\times 25}{36}\sqrt{2\times 36}$$

Multiply 2 and 36 to get 72.

$$\frac{x\times 25}{36}\sqrt{72}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{x\times 25}{36}\times 6\sqrt{2}$$

Cancel out 36, the greatest common factor in 6 and 36.

$$\frac{x\times 25}{6}\sqrt{2}$$

Express \frac{x\times 25}{6}\sqrt{2} as a single fraction.

$$\frac{x\times 25\sqrt{2}}{6}$$

Differentiate w.r.t. x

$$\frac{25 \sqrt{2}}{6} = 5.892556509887896$$