Solve sqrt{40/3}

$$\sqrt { \frac { 40 } { 3 } }$$

Evaluate

$$\frac{2\sqrt{30}}{3}\approx 3.651483717$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{40}{3}} as the division of square roots \frac{\sqrt{40}}{\sqrt{3}}.

$$\frac{\sqrt{40}}{\sqrt{3}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{2\sqrt{10}}{\sqrt{3}}$$

Rationalize the denominator of \frac{2\sqrt{10}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{10}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{10}\sqrt{3}}{3}$$

To multiply \sqrt{10} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{2\sqrt{30}}{3}$$