Solve sqrt{60/639299}

$$\sqrt{ \frac{ 60 }{ 639299 } }$$

Evaluate

$$\frac{2\sqrt{9589485}}{639299}\approx 0.009687765$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{60}{639299}} as the division of square roots \frac{\sqrt{60}}{\sqrt{639299}}.

$$\frac{\sqrt{60}}{\sqrt{639299}}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$\frac{2\sqrt{15}}{\sqrt{639299}}$$

Rationalize the denominator of \frac{2\sqrt{15}}{\sqrt{639299}} by multiplying numerator and denominator by \sqrt{639299}.

$$\frac{2\sqrt{15}\sqrt{639299}}{\left(\sqrt{639299}\right)^{2}}$$

The square of \sqrt{639299} is 639299.

$$\frac{2\sqrt{15}\sqrt{639299}}{639299}$$

To multiply \sqrt{15} and \sqrt{639299}, multiply the numbers under the square root.

$$\frac{2\sqrt{9589485}}{639299}$$