Solve sqrt{8/15}

$$\sqrt { \frac { 8 } { 15 } }$$

Evaluate

$$\frac{2\sqrt{30}}{15}\approx 0.730296743$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{8}{15}} as the division of square roots \frac{\sqrt{8}}{\sqrt{15}}.

$$\frac{\sqrt{8}}{\sqrt{15}}$$

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}.

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

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

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

The square of \sqrt{15} is 15.

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

To multiply \sqrt{2} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{2\sqrt{30}}{15}$$