Solve sqrt{69.695/14.4}=?

$$\sqrt { \frac { 69.695 } { 14.4 } } = ?$$

Evaluate

$$\frac{\sqrt{69695}}{120}\approx 2.199984217$$

Solution Steps

Expand \frac{69.695}{14.4} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{69695}{14400}}$$

Reduce the fraction \frac{69695}{14400} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{13939}{2880}}$$

Rewrite the square root of the division \sqrt{\frac{13939}{2880}} as the division of square roots \frac{\sqrt{13939}}{\sqrt{2880}}.

$$\frac{\sqrt{13939}}{\sqrt{2880}}$$

Factor 2880=24^{2}\times 5. Rewrite the square root of the product \sqrt{24^{2}\times 5} as the product of square roots \sqrt{24^{2}}\sqrt{5}. Take the square root of 24^{2}.

$$\frac{\sqrt{13939}}{24\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{13939}}{24\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{13939}\sqrt{5}}{24\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{13939}\sqrt{5}}{24\times 5}$$

To multiply \sqrt{13939} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{69695}}{24\times 5}$$

Multiply 24 and 5 to get 120.

$$\frac{\sqrt{69695}}{120}$$