Solve sqrt{123658/233}

$$\sqrt{ \frac{ 123658 }{ 233 } }$$

Evaluate

$$\frac{\sqrt{28812314}}{233}\approx 23.037383316$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{123658}{233}} as the division of square roots \frac{\sqrt{123658}}{\sqrt{233}}.

$$\frac{\sqrt{123658}}{\sqrt{233}}$$

Rationalize the denominator of \frac{\sqrt{123658}}{\sqrt{233}} by multiplying numerator and denominator by \sqrt{233}.

$$\frac{\sqrt{123658}\sqrt{233}}{\left(\sqrt{233}\right)^{2}}$$

The square of \sqrt{233} is 233.

$$\frac{\sqrt{123658}\sqrt{233}}{233}$$

To multiply \sqrt{123658} and \sqrt{233}, multiply the numbers under the square root.

$$\frac{\sqrt{28812314}}{233}$$