Solve sqrt{50/3*0.8}

$$\sqrt{ \frac{ 50 }{ 3 \times 0.8 } }$$

Evaluate

$$\frac{5\sqrt{30}}{6}\approx 4.564354646$$

Solution Steps

Multiply 3 and 0.8 to get 2.4.

$$\sqrt{\frac{50}{2.4}}$$

Expand \frac{50}{2.4} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{500}{24}}$$

Reduce the fraction \frac{500}{24} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{125}{6}}$$

Rewrite the square root of the division \sqrt{\frac{125}{6}} as the division of square roots \frac{\sqrt{125}}{\sqrt{6}}.

$$\frac{\sqrt{125}}{\sqrt{6}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

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

Rationalize the denominator of \frac{5\sqrt{5}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{5\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

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

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{5\sqrt{30}}{6}$$