Solve 5sqrt{2div6}

$$5 \sqrt{ 2 \div 6 }$$

Evaluate

$$\frac{5\sqrt{3}}{3}\approx 2.886751346$$

Solution Steps

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$5\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$5\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$5\times \frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Express 5\times \frac{\sqrt{3}}{3} as a single fraction.

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