Solve xsqrt{1/231}

$$x \sqrt { \frac { 1 } { 231 } }$$

Evaluate

$$\frac{\sqrt{231}x}{231}$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{231}} as the division of square roots \frac{\sqrt{1}}{\sqrt{231}}.

$$x\times \frac{\sqrt{1}}{\sqrt{231}}$$

Calculate the square root of 1 and get 1.

$$x\times \frac{1}{\sqrt{231}}$$

Rationalize the denominator of \frac{1}{\sqrt{231}} by multiplying numerator and denominator by \sqrt{231}.

$$x\times \frac{\sqrt{231}}{\left(\sqrt{231}\right)^{2}}$$

The square of \sqrt{231} is 231.

$$x\times \frac{\sqrt{231}}{231}$$

Express x\times \frac{\sqrt{231}}{231} as a single fraction.

$$\frac{x\sqrt{231}}{231}$$

Differentiate w.r.t. x

$$\frac{\sqrt{231}}{231} = 0.0657951694959769$$