Solve sqrt{78392/6}

$$\sqrt{ \frac{ 78392 }{ 6 } }$$

Evaluate

$$\frac{2\sqrt{29397}}{3}\approx 114.303689063$$

Solution Steps

Reduce the fraction \frac{78392}{6} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{39196}{3}}$$

Rewrite the square root of the division \sqrt{\frac{39196}{3}} as the division of square roots \frac{\sqrt{39196}}{\sqrt{3}}.

$$\frac{\sqrt{39196}}{\sqrt{3}}$$

Factor 39196=2^{2}\times 9799. Rewrite the square root of the product \sqrt{2^{2}\times 9799} as the product of square roots \sqrt{2^{2}}\sqrt{9799}. Take the square root of 2^{2}.

$$\frac{2\sqrt{9799}}{\sqrt{3}}$$

Rationalize the denominator of \frac{2\sqrt{9799}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{9799}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{9799}\sqrt{3}}{3}$$

To multiply \sqrt{9799} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{2\sqrt{29397}}{3}$$