Solve c^2/sqrt{208}

$$\frac { c ^ { 2 } } { \sqrt { 208 } }$$

Evaluate

$$\frac{\sqrt{13}c^{2}}{52}$$

Solution Steps

Factor 208=4^{2}\times 13. Rewrite the square root of the product \sqrt{4^{2}\times 13} as the product of square roots \sqrt{4^{2}}\sqrt{13}. Take the square root of 4^{2}.

$$\frac{c^{2}}{4\sqrt{13}}$$

Rationalize the denominator of \frac{c^{2}}{4\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{c^{2}\sqrt{13}}{4\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{c^{2}\sqrt{13}}{4\times 13}$$

Multiply 4 and 13 to get 52.

$$\frac{c^{2}\sqrt{13}}{52}$$

Differentiate w.r.t. c

$$\frac{\sqrt{13}c}{26}$$