Solve frac{3+sqrt{600}c}{300/6}

$$\frac { 3 + \sqrt { 600 } c } { \frac { 300 } { 6 } }$$

Evaluate

$$\frac{\sqrt{6}c}{5}+\frac{3}{50}$$

Solution Steps

Divide 3+\sqrt{600}c by \frac{300}{6} by multiplying 3+\sqrt{600}c by the reciprocal of \frac{300}{6}.

$$\frac{\left(3+\sqrt{600}c\right)\times 6}{300}$$

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$\frac{\left(3+10\sqrt{6}c\right)\times 6}{300}$$

Divide \left(3+10\sqrt{6}c\right)\times 6 by 300 to get \left(3+10\sqrt{6}c\right)\times \frac{1}{50}.

$$\left(3+10\sqrt{6}c\right)\times \frac{1}{50}$$

Use the distributive property to multiply 3+10\sqrt{6}c by \frac{1}{50}.

$$3\times \frac{1}{50}+10\sqrt{6}c\times \frac{1}{50}$$

Multiply 3 and \frac{1}{50} to get \frac{3}{50}.

$$\frac{3}{50}+10\sqrt{6}c\times \frac{1}{50}$$

Multiply 10 and \frac{1}{50} to get \frac{10}{50}.

$$\frac{3}{50}+\frac{10}{50}\sqrt{6}c$$

Reduce the fraction \frac{10}{50} to lowest terms by extracting and canceling out 10.

$$\frac{3}{50}+\frac{1}{5}\sqrt{6}c$$

Differentiate w.r.t. c

$$\frac{\sqrt{6}}{5} = 0.4898979485566356$$