Solve sqrt{2,5/1,28}

$$\sqrt { \frac { 2,5 } { 1,28 } }$$

Evaluate

$$\frac{5\sqrt{5}}{8}\approx 1.397542486$$

Solution Steps

Expand \frac{2,5}{1,28} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{250}{128}}$$

Reduce the fraction \frac{250}{128} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{125}{64}}$$

Rewrite the square root of the division \sqrt{\frac{125}{64}} as the division of square roots \frac{\sqrt{125}}{\sqrt{64}}.

$$\frac{\sqrt{125}}{\sqrt{64}}$$

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}.

$$\frac{5\sqrt{5}}{\sqrt{64}}$$

Calculate the square root of 64 and get 8.

$$\frac{5\sqrt{5}}{8}$$