Solve sqrt{20/3}

$$\sqrt { \frac { 20 } { 3 } }$$

Evaluate

$$\frac{2\sqrt{15}}{3}\approx 2.581988897$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{20}{3}} as the division of square roots \frac{\sqrt{20}}{\sqrt{3}}.

$$\frac{\sqrt{20}}{\sqrt{3}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{2\sqrt{5}}{\sqrt{3}}$$

Rationalize the denominator of \frac{2\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{5}\sqrt{3}}{3}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{2\sqrt{15}}{3}$$