Solve frac{4sqrt{2}}{sqrt{77}}

$$\frac{ 4 \sqrt{ 2 } }{ \sqrt{ 77 } }$$

Evaluate

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

Solution Steps

Rationalize the denominator of \frac{4\sqrt{2}}{\sqrt{77}} by multiplying numerator and denominator by \sqrt{77}.

$$\frac{4\sqrt{2}\sqrt{77}}{\left(\sqrt{77}\right)^{2}}$$

The square of \sqrt{77} is 77.

$$\frac{4\sqrt{2}\sqrt{77}}{77}$$

To multiply \sqrt{2} and \sqrt{77}, multiply the numbers under the square root.

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