Solve =sqrt{400*200*160*40}m^2

$$= \sqrt { 400 \times 200 \times 160 \times 40 } m ^ { 2 }$$

Evaluate

$$16000\sqrt{2}m^{2}$$

Solution Steps

Multiply 400 and 200 to get 80000.

$$\sqrt{80000\times 160\times 40}m^{2}$$

Multiply 80000 and 160 to get 12800000.

$$\sqrt{12800000\times 40}m^{2}$$

Multiply 12800000 and 40 to get 512000000.

$$\sqrt{512000000}m^{2}$$

Factor 512000000=16000^{2}\times 2. Rewrite the square root of the product \sqrt{16000^{2}\times 2} as the product of square roots \sqrt{16000^{2}}\sqrt{2}. Take the square root of 16000^{2}.

$$16000\sqrt{2}m^{2}$$

Differentiate w.r.t. m

$$32000\sqrt{2}m$$