Solve sqrt{337121.19/5}

$$\sqrt{ \frac{ 337121.19 }{ 5 } }$$

Evaluate

$$\frac{9\sqrt{2080995}}{50}\approx 259.661776163$$

Solution Steps

Expand \frac{337121.19}{5} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{33712119}{500}}$$

Rewrite the square root of the division \sqrt{\frac{33712119}{500}} as the division of square roots \frac{\sqrt{33712119}}{\sqrt{500}}.

$$\frac{\sqrt{33712119}}{\sqrt{500}}$$

Factor 33712119=9^{2}\times 416199. Rewrite the square root of the product \sqrt{9^{2}\times 416199} as the product of square roots \sqrt{9^{2}}\sqrt{416199}. Take the square root of 9^{2}.

$$\frac{9\sqrt{416199}}{\sqrt{500}}$$

Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$\frac{9\sqrt{416199}}{10\sqrt{5}}$$

Rationalize the denominator of \frac{9\sqrt{416199}}{10\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{9\sqrt{416199}\sqrt{5}}{10\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{9\sqrt{416199}\sqrt{5}}{10\times 5}$$

To multiply \sqrt{416199} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{9\sqrt{2080995}}{10\times 5}$$

Multiply 10 and 5 to get 50.

$$\frac{9\sqrt{2080995}}{50}$$