Solve g/6sqrt{72}

$$\frac { g } { 6 \sqrt { 72 } }$$

Evaluate

$$\frac{\sqrt{2}g}{72}$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{g}{6\times 6\sqrt{2}}$$

Multiply 6 and 6 to get 36.

$$\frac{g}{36\sqrt{2}}$$

Rationalize the denominator of \frac{g}{36\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{g\sqrt{2}}{36\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{g\sqrt{2}}{36\times 2}$$

Multiply 36 and 2 to get 72.

$$\frac{g\sqrt{2}}{72}$$

Differentiate w.r.t. g

$$\frac{\sqrt{2}}{72} = 0.019641855032959656$$