Solve sqrt{200/6}

$$\sqrt{ \frac{ 200 }{ 6 } }$$

Evaluate

$$\frac{10\sqrt{3}}{3}\approx 5.773502692$$

Solution Steps

Reduce the fraction \frac{200}{6} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{100}{3}}$$

Rewrite the square root of the division \sqrt{\frac{100}{3}} as the division of square roots \frac{\sqrt{100}}{\sqrt{3}}.

$$\frac{\sqrt{100}}{\sqrt{3}}$$

Calculate the square root of 100 and get 10.

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

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

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

The square of \sqrt{3} is 3.

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