Solve sqrt{625/2596}

$$\sqrt { \frac { 625 } { 2596 } }$$

Evaluate

$$\frac{25\sqrt{649}}{1298}\approx 0.49066792$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{625}{2596}} as the division of square roots \frac{\sqrt{625}}{\sqrt{2596}}.

$$\frac{\sqrt{625}}{\sqrt{2596}}$$

Calculate the square root of 625 and get 25.

$$\frac{25}{\sqrt{2596}}$$

Factor 2596=2^{2}\times 649. Rewrite the square root of the product \sqrt{2^{2}\times 649} as the product of square roots \sqrt{2^{2}}\sqrt{649}. Take the square root of 2^{2}.

$$\frac{25}{2\sqrt{649}}$$

Rationalize the denominator of \frac{25}{2\sqrt{649}} by multiplying numerator and denominator by \sqrt{649}.

$$\frac{25\sqrt{649}}{2\left(\sqrt{649}\right)^{2}}$$

The square of \sqrt{649} is 649.

$$\frac{25\sqrt{649}}{2\times 649}$$

Multiply 2 and 649 to get 1298.

$$\frac{25\sqrt{649}}{1298}$$