Solve sqrt{36.5/17}

$$\sqrt{ \frac{ 36.5 }{ 17 } }$$

Evaluate

$$\frac{\sqrt{2482}}{34}\approx 1.465284554$$

Solution Steps

Expand \frac{36.5}{17} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{365}{170}}$$

Reduce the fraction \frac{365}{170} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{73}{34}}$$

Rewrite the square root of the division \sqrt{\frac{73}{34}} as the division of square roots \frac{\sqrt{73}}{\sqrt{34}}.

$$\frac{\sqrt{73}}{\sqrt{34}}$$

Rationalize the denominator of \frac{\sqrt{73}}{\sqrt{34}} by multiplying numerator and denominator by \sqrt{34}.

$$\frac{\sqrt{73}\sqrt{34}}{\left(\sqrt{34}\right)^{2}}$$

The square of \sqrt{34} is 34.

$$\frac{\sqrt{73}\sqrt{34}}{34}$$

To multiply \sqrt{73} and \sqrt{34}, multiply the numbers under the square root.

$$\frac{\sqrt{2482}}{34}$$