Solve sqrt{250/9}

$$\sqrt{ \frac{ 250 }{ 9 } }$$

Evaluate

$$\frac{5\sqrt{10}}{3}\approx 5.270462767$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{250}{9}} as the division of square roots \frac{\sqrt{250}}{\sqrt{9}}.

$$\frac{\sqrt{250}}{\sqrt{9}}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$\frac{5\sqrt{10}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{5\sqrt{10}}{3}$$