Solve p*1/sqrt{28}

$$p \cdot \frac { 1 } { \sqrt { 28 } }$$

Evaluate

$$\frac{\sqrt{7}p}{14}$$

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$p\times \frac{1}{2\sqrt{7}}$$

Rationalize the denominator of \frac{1}{2\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$p\times \frac{\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$p\times \frac{\sqrt{7}}{2\times 7}$$

Multiply 2 and 7 to get 14.

$$p\times \frac{\sqrt{7}}{14}$$

Express p\times \frac{\sqrt{7}}{14} as a single fraction.

$$\frac{p\sqrt{7}}{14}$$

Differentiate w.r.t. p

$$\frac{\sqrt{7}}{14} = 0.18898223650461363$$