Solve sqrt{1390/182}

$$\sqrt{ \frac{ 1390 }{ 182 } }$$

Evaluate

$$\frac{\sqrt{63245}}{91}\approx 2.763577869$$

Solution Steps

Reduce the fraction \frac{1390}{182} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{695}{91}}$$

Rewrite the square root of the division \sqrt{\frac{695}{91}} as the division of square roots \frac{\sqrt{695}}{\sqrt{91}}.

$$\frac{\sqrt{695}}{\sqrt{91}}$$

Rationalize the denominator of \frac{\sqrt{695}}{\sqrt{91}} by multiplying numerator and denominator by \sqrt{91}.

$$\frac{\sqrt{695}\sqrt{91}}{\left(\sqrt{91}\right)^{2}}$$

The square of \sqrt{91} is 91.

$$\frac{\sqrt{695}\sqrt{91}}{91}$$

To multiply \sqrt{695} and \sqrt{91}, multiply the numbers under the square root.

$$\frac{\sqrt{63245}}{91}$$