Solve 8/sqrt{11*sqrt{14}}

$$\frac { 8 } { \sqrt { 11 } \times \sqrt { 14 } }$$

Evaluate

$$\frac{4\sqrt{154}}{77}\approx 0.644658371$$

Solution Steps

To multiply \sqrt{11} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{8}{\sqrt{154}}$$

Rationalize the denominator of \frac{8}{\sqrt{154}} by multiplying numerator and denominator by \sqrt{154}.

$$\frac{8\sqrt{154}}{\left(\sqrt{154}\right)^{2}}$$

The square of \sqrt{154} is 154.

$$\frac{8\sqrt{154}}{154}$$

Divide 8\sqrt{154} by 154 to get \frac{4}{77}\sqrt{154}.

$$\frac{4}{77}\sqrt{154}$$