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

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

Evaluate

$$\frac{3\sqrt{36108390}}{4945}\approx 3.645516104$$

Solution Steps

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

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

Express 32859\times \frac{2}{4945} as a single fraction.

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

Multiply 32859 and 2 to get 65718.

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

Rewrite the square root of the division \sqrt{\frac{65718}{4945}} as the division of square roots \frac{\sqrt{65718}}{\sqrt{4945}}.

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

Factor 65718=3^{2}\times 7302. Rewrite the square root of the product \sqrt{3^{2}\times 7302} as the product of square roots \sqrt{3^{2}}\sqrt{7302}. Take the square root of 3^{2}.

$$\frac{3\sqrt{7302}}{\sqrt{4945}}$$

Rationalize the denominator of \frac{3\sqrt{7302}}{\sqrt{4945}} by multiplying numerator and denominator by \sqrt{4945}.

$$\frac{3\sqrt{7302}\sqrt{4945}}{\left(\sqrt{4945}\right)^{2}}$$

The square of \sqrt{4945} is 4945.

$$\frac{3\sqrt{7302}\sqrt{4945}}{4945}$$

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

$$\frac{3\sqrt{36108390}}{4945}$$