Solve frac{sqrt{39}}{sqrt{6}}

$$\frac { \sqrt { 39 } } { \sqrt { 6 } }$$

Evaluate

$$\frac{\sqrt{26}}{2}\approx 2.549509757$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{39}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{39}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{39}\sqrt{6}}{6}$$

To multiply \sqrt{39} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{234}}{6}$$

Factor 234=3^{2}\times 26. Rewrite the square root of the product \sqrt{3^{2}\times 26} as the product of square roots \sqrt{3^{2}}\sqrt{26}. Take the square root of 3^{2}.

$$\frac{3\sqrt{26}}{6}$$

Divide 3\sqrt{26} by 6 to get \frac{1}{2}\sqrt{26}.

$$\frac{1}{2}\sqrt{26}$$