Solve sqrt{8div71}

$$\sqrt{ 8 \div 71 }$$

Evaluate

$$\frac{2\sqrt{142}}{71}\approx 0.335672543$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{8}{71}} as the division of square roots \frac{\sqrt{8}}{\sqrt{71}}.

$$\frac{\sqrt{8}}{\sqrt{71}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\sqrt{2}}{\sqrt{71}}$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{71}} by multiplying numerator and denominator by \sqrt{71}.

$$\frac{2\sqrt{2}\sqrt{71}}{\left(\sqrt{71}\right)^{2}}$$

The square of \sqrt{71} is 71.

$$\frac{2\sqrt{2}\sqrt{71}}{71}$$

To multiply \sqrt{2} and \sqrt{71}, multiply the numbers under the square root.

$$\frac{2\sqrt{142}}{71}$$