Solve 4sqrt{638/348}

$$4 \sqrt{ \frac{ 638 }{ 348 } }$$

Evaluate

$$\frac{2\sqrt{66}}{3}\approx 5.416025603$$

Solution Steps

Reduce the fraction \frac{638}{348} to lowest terms by extracting and canceling out 58.

$$4\sqrt{\frac{11}{6}}$$

Rewrite the square root of the division \sqrt{\frac{11}{6}} as the division of square roots \frac{\sqrt{11}}{\sqrt{6}}.

$$4\times \frac{\sqrt{11}}{\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{11}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$4\times \frac{\sqrt{11}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$4\times \frac{\sqrt{11}\sqrt{6}}{6}$$

To multiply \sqrt{11} and \sqrt{6}, multiply the numbers under the square root.

$$4\times \frac{\sqrt{66}}{6}$$

Express 4\times \frac{\sqrt{66}}{6} as a single fraction.

$$\frac{4\sqrt{66}}{6}$$

Divide 4\sqrt{66} by 6 to get \frac{2}{3}\sqrt{66}.

$$\frac{2}{3}\sqrt{66}$$