Solve f_{V}frac{sqrt{8}+5sqrt{32}-4sqrt{50}}{2}=

$$f _ { V } \frac { \sqrt { 8 } + 5 \sqrt { 32 } - 4 \sqrt { 50 } } { 2 } =$$

Evaluate

$$\sqrt{2}f_{V}$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$f_{V}\times \frac{2\sqrt{2}+5\sqrt{32}-4\sqrt{50}}{2}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$f_{V}\times \frac{2\sqrt{2}+5\times 4\sqrt{2}-4\sqrt{50}}{2}$$

Multiply 5 and 4 to get 20.

$$f_{V}\times \frac{2\sqrt{2}+20\sqrt{2}-4\sqrt{50}}{2}$$

Combine 2\sqrt{2} and 20\sqrt{2} to get 22\sqrt{2}.

$$f_{V}\times \frac{22\sqrt{2}-4\sqrt{50}}{2}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$f_{V}\times \frac{22\sqrt{2}-4\times 5\sqrt{2}}{2}$$

Multiply -4 and 5 to get -20.

$$f_{V}\times \frac{22\sqrt{2}-20\sqrt{2}}{2}$$

Combine 22\sqrt{2} and -20\sqrt{2} to get 2\sqrt{2}.

$$f_{V}\times \frac{2\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$f_{V}\sqrt{2}$$

Differentiate w.r.t. f_V

$$\sqrt{2} = 1.414213562$$