Solve sqrt{6550,02/182}

$$\sqrt { \frac { 6550,02 } { 182 } }$$

Evaluate

$$\frac{3\sqrt{3311399}}{910}\approx 5.999093338$$

Solution Steps

Expand \frac{6550,02}{182} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{655002}{18200}}$$

Reduce the fraction \frac{655002}{18200} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{327501}{9100}}$$

Rewrite the square root of the division \sqrt{\frac{327501}{9100}} as the division of square roots \frac{\sqrt{327501}}{\sqrt{9100}}.

$$\frac{\sqrt{327501}}{\sqrt{9100}}$$

Factor 327501=3^{2}\times 36389. Rewrite the square root of the product \sqrt{3^{2}\times 36389} as the product of square roots \sqrt{3^{2}}\sqrt{36389}. Take the square root of 3^{2}.

$$\frac{3\sqrt{36389}}{\sqrt{9100}}$$

Factor 9100=10^{2}\times 91. Rewrite the square root of the product \sqrt{10^{2}\times 91} as the product of square roots \sqrt{10^{2}}\sqrt{91}. Take the square root of 10^{2}.

$$\frac{3\sqrt{36389}}{10\sqrt{91}}$$

Rationalize the denominator of \frac{3\sqrt{36389}}{10\sqrt{91}} by multiplying numerator and denominator by \sqrt{91}.

$$\frac{3\sqrt{36389}\sqrt{91}}{10\left(\sqrt{91}\right)^{2}}$$

The square of \sqrt{91} is 91.

$$\frac{3\sqrt{36389}\sqrt{91}}{10\times 91}$$

To multiply \sqrt{36389} and \sqrt{91}, multiply the numbers under the square root.

$$\frac{3\sqrt{3311399}}{10\times 91}$$

Multiply 10 and 91 to get 910.

$$\frac{3\sqrt{3311399}}{910}$$