Solve sqrt{50/3}

$$\sqrt { \frac { 50 } { 3 } }$$

Evaluate

$$\frac{5\sqrt{6}}{3}\approx 4.082482905$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{50}{3}} as the division of square roots \frac{\sqrt{50}}{\sqrt{3}}.

$$\frac{\sqrt{50}}{\sqrt{3}}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

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

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

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{5\sqrt{6}}{3}$$