Solve sqrt{8/5}

$$\sqrt{ \frac{ 8 }{ 5 } }$$

Evaluate

$$\frac{2\sqrt{10}}{5}\approx 1.264911064$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{8}{5}} as the division of square roots \frac{\sqrt{8}}{\sqrt{5}}.

$$\frac{\sqrt{8}}{\sqrt{5}}$$

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}.

$$\frac{2\sqrt{2}}{\sqrt{5}}$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

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

The square of \sqrt{5} is 5.

$$\frac{2\sqrt{2}\sqrt{5}}{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{2\sqrt{10}}{5}$$