Solve sqrt{2704div3.4}

$$\sqrt{ 2704 \div 3.4 }$$

Evaluate

$$\frac{52\sqrt{85}}{17}\approx 28.200959516$$

Solution Steps

Expand \frac{2704}{3.4} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{27040}{34}}$$

Reduce the fraction \frac{27040}{34} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{13520}{17}}$$

Rewrite the square root of the division \sqrt{\frac{13520}{17}} as the division of square roots \frac{\sqrt{13520}}{\sqrt{17}}.

$$\frac{\sqrt{13520}}{\sqrt{17}}$$

Factor 13520=52^{2}\times 5. Rewrite the square root of the product \sqrt{52^{2}\times 5} as the product of square roots \sqrt{52^{2}}\sqrt{5}. Take the square root of 52^{2}.

$$\frac{52\sqrt{5}}{\sqrt{17}}$$

Rationalize the denominator of \frac{52\sqrt{5}}{\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{52\sqrt{5}\sqrt{17}}{\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{52\sqrt{5}\sqrt{17}}{17}$$

To multiply \sqrt{5} and \sqrt{17}, multiply the numbers under the square root.

$$\frac{52\sqrt{85}}{17}$$