Solve sqrt{32859/4945{frac{2/9}}}

$$\sqrt{ \frac{ 32859 }{ \frac{ 4945 }{ \frac{ 2 }{ 9 } } } }$$

Evaluate

$$\frac{\sqrt{36108390}}{4945}\approx 1.215172035$$

Solution Steps

Divide 32859 by \frac{4945}{\frac{2}{9}} by multiplying 32859 by the reciprocal of \frac{4945}{\frac{2}{9}}.

$$\sqrt{\frac{32859\times \frac{2}{9}}{4945}}$$

Express 32859\times \frac{2}{9} as a single fraction.

$$\sqrt{\frac{\frac{32859\times 2}{9}}{4945}}$$

Multiply 32859 and 2 to get 65718.

$$\sqrt{\frac{\frac{65718}{9}}{4945}}$$

Divide 65718 by 9 to get 7302.

$$\sqrt{\frac{7302}{4945}}$$

Rewrite the square root of the division \sqrt{\frac{7302}{4945}} as the division of square roots \frac{\sqrt{7302}}{\sqrt{4945}}.

$$\frac{\sqrt{7302}}{\sqrt{4945}}$$

Rationalize the denominator of \frac{\sqrt{7302}}{\sqrt{4945}} by multiplying numerator and denominator by \sqrt{4945}.

$$\frac{\sqrt{7302}\sqrt{4945}}{\left(\sqrt{4945}\right)^{2}}$$

The square of \sqrt{4945} is 4945.

$$\frac{\sqrt{7302}\sqrt{4945}}{4945}$$

To multiply \sqrt{7302} and \sqrt{4945}, multiply the numbers under the square root.

$$\frac{\sqrt{36108390}}{4945}$$