Solve sqrt{783.92/6}

$$\sqrt{ \frac{ 783.92 }{ 6 } }$$

Evaluate

$$\frac{\sqrt{29397}}{15}\approx 11.430368906$$

Solution Steps

Expand \frac{783.92}{6} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{78392}{600}}$$

Reduce the fraction \frac{78392}{600} to lowest terms by extracting and canceling out 8.

$$\sqrt{\frac{9799}{75}}$$

Rewrite the square root of the division \sqrt{\frac{9799}{75}} as the division of square roots \frac{\sqrt{9799}}{\sqrt{75}}.

$$\frac{\sqrt{9799}}{\sqrt{75}}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{\sqrt{9799}}{5\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{9799}}{5\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{9799}\sqrt{3}}{5\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{9799}\sqrt{3}}{5\times 3}$$

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

$$\frac{\sqrt{29397}}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$\frac{\sqrt{29397}}{15}$$